Hsiang received in 1957 his bachelor's degree from the National Taiwan University and in 1963 his Ph.D. under Norman Steenrod from Princeton University with thesis Obstructions to sectioning fibre bundles. At Yale University he became in 1962 a lecturer, in 1963 an assistant professor, and in 1968 a full professor. At Princeton University he was a full professor from 1972 until retiring in 2006 as professor emeritus and was the department chair from 1982 to 1985. He was a visiting scholar at the Institute for Advanced Study for the academic years 1965–1966, 1971–1972, and 1979–1980. He was a visiting professor at the University of Warwick in 1966, the University of Amsterdam in 1969, the University of Bonn in 1971, the University of California, Berkeley in 1976, and the Mathematical Sciences Research Institute and Stanford University in 1980.
Hsiang has made important contributions to algebraic and differential topology. Works by Hsiang, Julius Shaneson, C. T. C. Wall, Robion Kirby, Laurent Siebenmann and Andrew Casson led in the 1960s to the proof of the annulus theorem (previously known as the annulus conjecture). The annulus theorem is important in the theory of triangulation of manifolds.
With F. Thomas Farrell he worked on a program to prove the Novikov conjecture and the Borel conjecture with methods from geometric topology and gave proofs for special cases. For example, they gave a proof of the integral Novikov conjecture for compact Riemannian manifolds with non-positive sectional curvature. Hsiang also made contributions to the topological study of simply-connected 4-manifolds.
From 1967 to 1969 he was a Sloan Fellow and for the academic year 1975–1976 a Guggenheim Fellow. In 1980 he was elected a member of Academia Sinica. He was an Invited Speaker at the International Congress of Mathematicians in 1970 in Nice, with a talk on Differentiable actions of compact connected Lie groups on  and a Plenary Speaker in 1983 in Warsaw, with a talk on Geometric applications of algebraic K-theory. In 2005 there was a conference at Stanford University in honor of his 70th birthday.
- Wu-Chung Hsiang at the Mathematics Genealogy Project
- "Eight faculty members transfer to emeritus status". Princeton Weekly Bulletin. 95 (29). Princeton University. 19 June 2006.
- Hsiang, Wu-Chung and Shaneson, Julius L. (1969). Fake tori, the annulus conjecture, and the conjectures of Kirby. Proceedings of the National Academy of Sciences of the United States of America, 62 (3), 687–691.
- Hsiang, Wu-Chung: Borel's conjecture, Novikov's conjecture and K-theoretic analogues, in: Algebra, Analysis and Topology, World Scientific 1989
- Farrell, F. Thomas; Hsiang, Wu-Chung (1981). "On Novikov's conjecture for non-positively curved manifolds, I". Annals of Mathematics. 113: 199–209. doi:10.2307/1971138. JSTOR 1971138.
- Curtis, Cynthia L.; Freedman, Michael H.; Hsiang, Wu-Chung; Stong, Richard (1996). "A decomposition theorem for h-cobordant smooth simply-connected compact 4-manifolds". Inventiones Mathematicae. 123 (2): 343–348. doi:10.1007/s002220050031. MR 1374205.
- Hsiang, Wu-Chung. "Differentiable actions of compact connected Lie groups on ." Actes Congr. Int. Mathématiciens (1970): 73–77.
- Hsiang, Wu-Chung. "Geometric applications of algebraic K-theory." In Proceedings of the International Congress of Mathematicians, vol. 1, p. 2. 1983.
- Algebraic & Differential Topology: A Conference in Honor of Wu-chung's 70th Birthday, Stanford U., August 6th and 7th, 2005