If $K[G]$ denotes the group algebra of G over the field K, then the trace map $tr : K[G] \to K$ picks off the identity coefficient of each element of the ring. In this talk, I will discuss what is known about traces of algebraic elements of $K[G]$. Of particular interest are the traces of idempotents and nilpotent elements. If time permits, I will also consider analogous results for twisted group algebras.