Puiseux series are named after him, as is in part the Bertrand–Diquet–Puiseux theorem.
His work on algebraic functions and uniformization makes him a direct precursor of Bernhard Riemann, for what concerns the latter's work on this subject and his introduction of Riemann surfaces.
A species of gecko, Ptyodactylus puiseuxi, is named in his honor.
Excelling in mathematical analysis, he introduced new methods in his account of algebraic functions, and by his contributions to celestial mechanics advanced knowledge in that direction.
One of his sons, Pierre Henri Puiseux, was a famous astronomer.