The invention generally relates to functional polymers and hydrogels. More particularly, the invention provides versatile monomers and polymers with well-defined functionalities, e.g., polycarbonates and poly(ester-carbonates), compositions thereof, and methods for making and using the same. The invention also provides cytocompatible poly(ethylene glycol)-co-polycarobonate hydrogels (e.g., crosslinked by copper-free, strain-promoted “click” chemistry).