Semipermeable membranes are the core elements for membrane water desalination technologies such as commercial reverse osmosis (RO) process and emerging forward osmosis (FO) process. Structural and chemical properties of the semipermeable membranes determine water flux, salt rejection, fouling resistance, and chemical stability, which greatly impact energy consumption and costs in osmosis separation processes. In recent years, significant progress has been made in the development of high-performance polymer and polymer composite membranes for desalination applications. This paper reviews recent advances in different polymer-based RO and FO desalination membranes in terms of materials and strategies developed for improving properties and performances.