Weierstrass published his celebrated approximation theorems in July of 1885. I will start with brief speculations on the antecedents of Weierstrass' work and move on to a selective survey of results and/or proofs related to Weierstrass' original theorems. The survey will include results and/or proofs of Lebesgue, Landau, de la Vallee Poussin, Bernstein, Korovkin, and Stone, as time permits.