The historical period of Chavakuk is not mentioned in the text, but RADAK quotes Seder Olam as follows: "Yoel, Nachum and Chavakuk prophesied in the days of Menashe, but since (the King) Menashe was evil, they are not related to him."
His main Prophecy concerns Nevuchadnezzar, the evil King of the Chaldeans-Babylonians who, for a period of time, ruled the world until, in the time of his descendant Belshatzar, his Kingdom would be overthrown by the Persians and the Medes.
Nevuchadnezzar was bad enough, having destroyed Yerushalayim and the First Temple, but Chavakuk raises a question that is universal, encompassing all of human history. "Why do the wicked seem to prosper and the righteous to suffer?"
"This will weaken belief in the Torah, and cause Justice not ever to emerge, for the wicked surrounds the righteous; therefore does Justice come out perverted!" (Chavakuk, 1:4)
Kara explains "surrounds the righteous" as referring to Nevuchadnezzar, who exiled Israel three times: in the time of Yehoyakim, in the time of Yehoyachin and finally in the time of King Tzidkiyahu, when he put out all the King's sons' eyes in his presence, before destroying the City of Yerushalayim and burning the Holy Temple.
HaShem had raised this nation, the Kasdim, a nation "bitter of spirit and impetuous of judgment" (Chavakuk 1:6) to be a world-conquering nation, though they were a nation described in Yeshayahu as "a nation that never was," meaning that it was one "of three items in Creation that HaShem 'regretted' having brought into the world." (Masechet Sukkah)
That nation that "mocks kings and princes, laughs at fortifications because it can easily overcome them by building high earthen ramps to capture them " (Chavakuk 1:10)
Chavakuk cries out, "Are You not the Ancient of Days, my G-d, my Holy L-rd, Who is Eternal ?" (Chavakuk 1:12) Why do You let this illegitimate nation mock You as well, as it were?
Sifre explains that the expression for "Eternal," which should have been written "You will not die," referring to HaShem, was actually emended in the Text by the Scribes to read "We will not die," as a euphemism, to remove any association of death (G-d Forbid) from the Holy One. This is not a unique case; it occurs in a small number of documented instances in the Bible.
"You Who are too pure of eyes to see evil, and to behold iniquity, why do You nevertheless view traitors and remain silent when the wicked swallow the one who is more righteous than he?" (Chavakuk 1:13)
At the beginning of Chapter Two, Chavakuk declares that he will not move until he receives a response from the Almighty to his question. And then he records that HaShem responded, "Od Chazon LaMoed," "There shall yet be another vision at that time, that shall speak of the end, and it shall not fail, " (Chavakuk 2:3) referring to Yirmiyahu, who will prophecy the end of the Empire of the Kasdim-Babylonians, after seventy years of Exile of the Jewish People.
Now Chavakuk states, in the Name of HaShem, the principle discussed by Rabbi Simlai, at the end of Masechet Makkot. There in the Talmud, the Rabbi records how various great leaders of the Jewish People attempted to reduce, for educational purposes, the number of commandments of the Torah to a number fewer than 613: King David, to 11; Yeshayahu, to 6; Michah, to 3; Yehayahu again, this time to 2; finally Chavakuk, to 1; namely, "And the righteous shall live by his faith." (Chavakuk 2:4) This seems to mean that the human being should take into account the unbridgeable gap between himself and G-d, between the finite and mortal creation and the Infinite and Eternal Creator, and simply put his faith and trust in HaShem that His Justice, in the end, is Perfect.
Chapter 3 of Chavakuk begins, according to one interpretation, with a prayer from the Prophet that he be forgiven for questioning G-d's Justice. This Chapter is chosen as the Haftarah for the Second Day of Shavuot, the Second Day of the Holiday, as celebrated in the Diaspora.
The Prophet describes the event of "Matan Torah," the Giving of the Torah by HaShem to the Jewish People and hence to humanity in general, that is celebrated on that Day, as having been a once-in- history event, illuminating the entire remainder of human history, clearly revealing HaShem as the King and Supreme Judge of All the World.
According to the RAMBAM, Chavakuk was a link in the Chain of "Mesorah," and received the Tradition of Torah from Yoel and his court.