This paper studies lower bounds for classical multicolor Ramsey numbers, first by giving a short overview of past results, and then by presenting several general constructions establishing new lower bounds for many diagonal and off-diagonal multicolor Ramsey numbers. In particular, we improve several lower bounds for R_k(4) and R_k(5) for some small k, including 415 \u3c = R_3(5), 634 \u3c = R_4(4), 2721 \u3c = R_4(5), 3416 \u3c = R_5(4) and 26082 \u3c = R_5(5). Most of the new lower bounds are consequences of general constructions
