Steven Krantz grew up in Redwood City, California and graduated from Sequoia High School in class of 1967.

[1] Krantz was an undergraduate at the University of California, Santa Cruz (UCSC), graduating with summa cum laude in 1971.

In the mathematics department at UCSC his teachers included Nick Burgoyne, Marvin Greenberg, Ed Landesman, and Stan Philipp.

Krantz obtained his Ph.D. in mathematics from Princeton University in 1974 under the direction of Elias M. Stein and Joseph J. Kohn.

Krantz's book on the geometry of complex domains, written jointly with Robert E. Greene and Kang-Tae Kim, appeared in 2011.

Among the latter are Xiaojun Huang (holder of the Bergman Prize), Marco Peloso, Fausto Di Biase, Daowei Ma, and Siqi Fu.

Krantz has organized conferences, including the Summer Workshop in Several Complex Variables held in Santa Cruz in 1989 and attended by 250 people.

He organized and spoke at a conference on the corona problem held at the Fields Institute in Toronto, Canada in June 2012.