The Feynman rules are derived for massless particles of arbitrary spin j. The rules are the same as those presented in an earlier article for m>0, provided that we let m-->0 in propagators and wave functions, and provided that we keep to the (2j+1)-component formalism [with fields of the (j, 0) or (0, j) type] or the 2(2j+1)-component formalism [with (j, 0)⊕(0, j) fields]. But there are other field types which cannot be constructed for m=0; these include the (j2, j2) tensor fields, and in particular the vector potential for j=1. This restriction arises from the non-semi-simple structure of the little group for m=0. Some other subjects discussed include: T, C, and P for massless particles and fields; the extent to which chirality conservation implies zero physical mass; and the Feynman rules for massive particles in the helicity formalism. Our approach is based on the assumption that the S matrix is Lorentz invariant, and makes no use of Lagrangians or the canonical formalism.