Rabbi Tzvi Hirsch ben Yaakov Ashkenazi, the Chacham Tzvi, was born in Moravia, in Trebitsch according to the Hebrew Wikipedia and most likely in Gross Meseritsch according to the English one, the son of Rabbi Yaakov ben Binyamin Zak and Nechama, daughter of Rabbi Ephraim HaKohen, author of Shaar Ephraim. His family had fled the massacres of 1648 in Poland and Lithuania. He first studied with his father and, from the age of eight, in Ofen (Buda) with his grandfather, the city's rabbi. In 5433 (1673) he went to Salonika, where he studied for two years under Rabbi Eliyahu Covo and absorbed the Sephardic method of study; he kept the Sephardic title of Chacham for the rest of his life.

Back in Ofen he married, but in 1686, during the siege of the city by the Austrian army, a cannonball destroyed his house and killed his wife and little daughter. He fled to Sarajevo, where he served as rabbi of the community until 1689, then set out in search of his parents, who had been taken captive and ransomed in Berlin, passing through Venice, Ansbach, Fuerth and Prague. In Berlin he married Sarah Rivka, daughter of Rabbi Meshullam Zalman Mirels Neumark, rabbi of the three communities of Altona, Hamburg and Wandsbek. He settled in Altona for eighteen years, founded a yeshiva and a renowned kloyz there, and in 5466 was appointed rabbi of the three communities, alternating six-month terms with Rabbi Moshe Rothenburg; a halachic controversy over a hen found without a heart forced him to resign.

In 1710 he was called to the chief rabbinate of the Ashkenazi community of Amsterdam with a salary of 2,500 guilders, ten times the usual amount elsewhere; Ashkenazim and Sephardim alike held him in great esteem. There, in 5472 (1712), he printed his collection of responsa and novellae, Sheelot uTeshuvot Chacham Tzvi, which remains a classic. A resolute opponent of Sabbateanism, in 5473 he fought Nechemia Chiya Chayun, who sought to print his book Divrei Nechemia; the ensuing conflict with the Sephardic community of Rabbi Shlomo Ayllon, which accused him of interfering in its affairs, forced him to leave Amsterdam together with Rabbi Moshe Chagiz, who had supported him.

He sent his family to Emden and travelled to England at the invitation of the Sephardic community of London, which had earlier consulted him about its preacher Rabbi David Nieto. He then passed through many communities in Germany and Poland before arriving, in the winter of 5478, in Lemberg (Lviv) in Galicia, where he served as rabbi for a few months and enacted several important ordinances. In his learning he combined the Sephardic and Ashkenazi methods. He had sixteen children, among them Rabbi Yaakov Emden, the Yaavetz, who wrote his biography in Megillat Sefer and Torat HaKenaot.

He passed away in Lemberg on 1 Iyar 5478 (1718) and rests there in the old Jewish cemetery. His son Rabbi Yaakov Emden came to deliver his eulogy, printed under the title Yatziv Pitgam.