The custom of learning Torah through the night of Shavuot is a young one, by Jewish standards. Before the 1500s, it's possible that it was never practiced at all, or perhaps only by a few. Although there are some ideas that prefigure the custom in the Midrash and early commentators on the Torah, the idea of Tikkun Leil Shavuot really has its main root in the Zohar.
וְאוֹלִיפְנָא, דְּאוֹרַיְיתָא דְּבָעֵי לֵיהּ לְמִלְעֵי בְּהַאי לֵילְיָא, אוֹרַיְיתָא דְבְּעַל פֶּה, בְּגִין דְּיִתְדְּכוּן (ס''א דיתדבק) כַּחֲדָא, מִמַּבּוּעָא דְּנַחֲלָא עֲמִיקָא. לְבָתַר, בְּהַאי יוֹמָא, לֵיתֵי תּוֹרָה שֶׁבִּכְתָּב, וְיִתְחַבֵּר (ס''א בהו) בָּהּ, וְיִשְׁתַּכְחוּן כַּחֲדָא בְּזִוּוּגָא חַד לְעֵילָּא. כְּדֵין מַכְרִיזֵי עָלֵיהּ וְאַמְרֵי, (ישעיהו נ״ט:כ״א) וַאֲנִי זֹאת בְּרִיתִי אוֹתָם אָמַר ה'' רוּחִי אֲשֶׁר עָלֶיךָ וּדְבָרַי אֲשֶׁר שַׂמְתִּי בְּפִיךָ וְגוֹ'.
וְעַל דָּא, חֲסִידֵי קַדְמָאֵי לָא הֲווֹ נָיְימֵי בְּהַאי לֵילְיָא, וַהֲווּ לָעָאן בְּאוֹרַיְיתָא, וְאַמְרֵי, נֵיתֵי לְאַחֲסָנָא יְרוּתָא קַדִּישָׁא, לָן, וְלִבְנָן, בִּתְרֵין עָלְמִין. וְהַהוּא לֵילְיָא כְּנֶסֶת יִשְׂרָאֵל אִתְעַטְּרָא עָלַיְיהוּ, וְאַתְיָיא לְאִזְדַּוְּוגָא בֵּיהּ בְּמַלְכָּא, וְתַרְוַויְיהוּ מִתְעַטְּרֵי עַל רֵישַׁיְיהוּ, דְּאִינּוּן דְּזַכָּאן לְהָכִי.
We have learned that the Torah that we need to learn on this night [Leyl Shavuot] is the Oral Torah, so that they may be purified together from the wellspring of the deep stream. Afterward, on this day [of Shavuot] Written Torah will come join her and they will be as one, as one couple above. Then it is proclaimed about him (Isaiah 59:21) 'And this is for Me My covenant with them said Hashem: My spirit that is upon you and My words I have put in your mouth (will not depart from your mouth, nor from your children's mouths...now and forever)'.
Thus, the earlier pious ones did not sleep on this night, and they studied Torah, saying let us acquire a holy inheritance for us and our children in two worlds. And on this night, Keneset Yisrael is crowned above them and comes to intimately join with the King, and both of them are crowned above the heads of those who are worthy of this.
The earliest recorded case of a Tikkun Leil Shavuot being practiced was in Greece, in the year 1533 (or thereabouts), and it was a remarkable one. Present were R. Yosef Karo, later the author of the Shulchan Aruch, R. Shlomo HaLevi Alkabetz, later the composer of Lecha Dodi, and other unnamed members of their circle. A few years later, R. Alkabetz wrote of the experience.
דעו לכם כי הסכמנו החסיד נר"ו ואני עבדו ועבידכם מהחברים לעמוד על נפשינו ליל שבועות ולנדד שינה מעינינו, ותהלות לה' כן עלה בידינו כי לא הפסקנו רגע רק אשר תשמעו ותחי נפשכם...
ובעת שהתחלנו ללמוד המשנה ולמדנו שתי מסכתות, זיכנו בוראנו ונשמע את קול המדבר בפי החסיד נר"ו קול גדול בחיתוך אותיות, וכל השכנים היו שומעים ולא מבינים, והיה הנעימות רב והקול הולך וחזק, ונפלנו על פנינו ולא היה רוח באיש לישא עיניו ופניו לראות מרוב המורא והדיבור ההוא מדבר עמנו והתחיל ואמר, שמעו ידידי המהדרים מן המהדרים, ידידי אהובי שלום לכם אשריכם ואשרי ילדתכם, אשריכם בעולם הזה אשריכם בעולם הבא אשר שמתם על נפשיכם לעטרני בלילה הזה אשר זה כמה שנים נפלה עטרת ראשי ואין מנחם לי, ואני מושלכת בעפר חובקת אשפתות, ועתה החזרתם עטרה ליושנה...
Know - that the pious one (R. Yosef Karo) and I agreed to make a great effort on the night of Shavuot, and to keep sleep from our eyes. Praise to God, so it was. We didn't stop one moment - listen, and your soul will be revived...
The moment that we began to learn the Mishnah, and we learned two mesechtot, our creator graced us and we heard a voice speaking from the mouth of the pious one. A great voice, with clear enunciation, and all around us heard but did not understand. It was very pleasant, and the voice gained strength. We fell on our faces, and none could raise their eyes from fear. The voice speaking to us began and said - "Hear my beloved ones, most beautiful, cherished, beloved, peace to you, fortunate are you and those that bore you, fortunate in this world and in the world to come, in that you took upon yourselves to crown me this night. It is many years that my crown has fallen from my head, and I have no one to comfort me, and I am cast to the dirt clutching waste. But you have returned the crown to its former glory...
ערב שבועות: ישנים שעה אחת או ב' שעות, אחר שעשו צרכי מועד, לפי שבלילה אחר האכילה מתקבצים בבתי כנסיות, כל קהל וקהל בב"ה שלו, ואינם ישנים כל הלילה, וקורין תורה נביאים וכתובים, ומשניות וזהר ודרשות בקראי עד אור הבוקר, ואז כל העם טובלים בבוקר קודם תפלת שחרית, כדאיתא בזוהר פ' אמור.
Avraham Galante (d. 1589)
The evening before Shavuot: they sleep an hour or two, after preparing the needs of the holiday, because on the night after the meal they gather in the synagogues, each community in its synagogue, and don't sleep the whole night. And they read Torah, Prophets, and Writings, Mishnah, Zohar, and Drashot on verses until the light of morning. Then the people immerse in the mikvah in the morning before Shacharit, as is written in the Zohar parshat Emor.
(יב) ודע, שכל מי שבלילה ההוא לא ישן כלל ועיקר ויהיה עוסק בתורה, מובטח לו שישלים שנתו, ולא יארע לו שום נזק, והוראת חיי האדם הוא בלילה זה:
(12) Know - that anyone who doesn't sleep at all on this night, and engages in Torah - it's guaranteed that he will live out the year and no harm will befall him, and the decree of a person's life is on this night.
In the next few centuries, the custom took hold and spread, until it became quite common. By the mid 1600s, the custom was already widespread. But how did it come to be that this practice became so popular?
Published in AJS Review, Vol. 14, No. 1 (Spring, 1989), pp. 17-46
Only in late-sixteenth-century Palestine did Tikkun Hazot [the custom of staying up until midnight] suddenly take off and become a mass rite, spreading from there to other countries in the Near East and the Mediterranean basin. Its popularization was, of course, part of the wider diffusion of kabbalistic rites during this period and their penetration into daily life, but it can hardly be divorced from the increasing availability, by day and night, of a stimulant such as coffee.
Although increasingly available, the beverage was not as universally familiar in the Near East of the sixteenth century as we might expect. R. Joseph Caro, for example, who came to Safed from Turkey in 1536 and completed his Bet Yosef there some six years later, shows no signs in the relevant sections of that work (nor of his later Shulkhan Arukh) of any familiarity with coffee. Yet Caro would have good reason to be interested in a stimulant which could effectively produce wakefulness. For he, together with his brother-in-law R. Solomon Alkabetz, introduced the custom of observing an all-night study vigil on the festival of Shavuot, and he also invested much energy in remaining awake at night on a year-round basis in order to commune with his personal "Maggid".
By 1580, however, there was at least one coffeehouse in Safed...
The roots of the custom to stay up at night seem rooted in the increasing influence of kabbalistic thought. R. Avraham Gombiner, the Magen Avraham, wrote in the mid 1600s. He seems uncomfortable with the mystical roots of the practice, and looks for a simpler reason.
(1) It says in the Zohar that the original pious ones would be awake all the night working in Torah. And already most of those who learn do this. It's possible to give a reason for this according to its simple understanding, that Israel slept all the night, and the Holy One Blessed be He had to wake them, as the midrash says. Therefore, we need to fix this.
The Midrash that the Magen Avraham draws from does have a critical element, though it could be read as offering a balanced view of sleep as well.
ר' פנחס בשם רבי הושעיא אמר: עד שהמלך במסבו עד שהמלך מלכי המלכים הקדוש ב"ה במסבו ברקיע. כבר הקדים, שנאמר: (שמות י"ט) ויהי ביום השלישי בהיות הבקר. למלך שגזר ליום פלוני, אני נכנס למדינה, וישנו להם בני המדינה כל הלילה. וכשבא המלך ומצאם ישנים, העמיד עליהם בקלאנין בוקינס ושופר, והיה השר של אותה מדינה, מעוררן ומוציאן לאפנתי של מלך, והיה המלך מהלך לפניהם, עד שהגיע לפלטין שלו. כך הקדוש ברוך הוא הקדים, דכתיב: ויהי ביום השלישי בהיות הבקר. וכתיב: כי ביום השלישי ירד ה' לעיני כל העם. ישנו להם ישראל כל אותו הלילה, לפי ששינה של עצרת עריבה והלילה קצרה. אמר ר' יודן: אפילו פורטענא לא עקץ בם. בא הקדוש ברוך הוא ומצאן ישנים, התחיל מעמיד עליהם בקלאנין. הדא הוא דכתיב: "ויהי ביום השלישי בהיות הבקר ויהי קולות וברקים". והיה משה מעורר לישראל ומוציאן, לאפנתי של מלך מלכי המלכים הקדוש ברוך הוא. הדא הוא דכתיב: ויוצא משה את העם לקראת האלקים. והיה הקדוש ברוך הוא מהלך לפניהם, עד שהגיע להר סיני. דכתיב: והר סיני עשן כלו. אמר רבי יצחק: זה הוא, שמקנתרן על ידי ישעיהו. שנאמר: (ישעיה נ') מדוע באתי ואין איש, קראתי ואין עונה, הקצר קצרה ידי מפדות?!
Rabbi Pinhas said in the name of Hoshaya: "While the king sat at his table": while the King of kings, the Holy One, Blessed Be He, sat at the heavens. He arrived early, as it is stated: (Exodus 19:16) "And it came to pass on the third day, when it was morning." This is like a king who decreed, "On such a day, I am going to enter the province." But the people of the province slept all through the night, so that when the king arrived and found them asleep, he set trumpets and horns to get them up. And the minister of that province woke them up and took them to meet the king. And the king walked before them, until he reached his palace. This is like the Holy One, Blessed Be He, as it is written: (Ibid.) "And it came to pass on the third day, when it was morning." And it written: (Ibid.) "For the third day the Lord will come down in the sight of the people." Israel slept all through the night, because the sleep of Shavuot is pleasant and the night is short. Rabbi Yudan said: Not even a flea stung them. When the Holy One, Blessed Be He, came and found them asleep, he started to get them up with trumpets, as it is written: (Exodus 16:16) "And it came to pass on the third day, when it was morning, that there were thunders and lightnings." And Moses roused Israel and took them to meet the King of kings, the Holy One, Blessed Be He, as it is written: (Exodus 19:17) "And Moses brought forth the people [out of the camp] to meet God." And the Holy One, Blessed Be He, went before them, until they reached Mount Sinai, as it is written: (Exodus 19:18): "Now mount Sinai was altogether on smoke." Rabbi Yitzkak said: It was this for which He chided them through [the prophesy of] Isaiah. As it is written: (Isaiah 50:2) "Wherefore, when I came, was there no man? When I called, was there no answer? Is My hand shortened at all, that it cannot redeem?"
Perhaps this midrash led to the following comment from Avraham Ibn Ezra (1089 - 1164 CE).
(1) Be Ready: Perhaps a person shouldn't sleep on them at night, because they will hear the voice of God in the morning...