Restricted projections is an exciting new theory that played an important role in recent developments in effective unipotent dynamics. It focuses on Marstrand-like projection theorems for certain Lebesgue-null non-degenerate (in some sense) submanifolds of the grassmannian. Using it, we establish new projection theorems for self-similar measures, which significantly refine the previous state-of-the-art results of Hochman-Shmerkin (2012) and Falconer-Jin (2014).