This paper surveys techniques for multiplying elements of various commutative rings. It covers Karatsuba multiplication, dual Karatsuba multiplication, Toom multiplication, dual Toom multiplication, the FFT trick, the twisted FFT trick, the split-radix FFT trick, Good's trick, the SchonhageStrassen trick, Schonhage's trick, Nussbaumer's trick, the cyclic SchonhageStrassen trick, and the Cantor-Kaltofen theorem. It emphasizes the underlying ring homomorphisms.