In this talk I will discuss algorithms for factoring polynomials over number fields to reach recent results on sparse polynomials, where the complexity of the algorithm takes into account the fact that the polynomial may have many zero coefficients. For simplicity I'll focus on rational polynomials in one or two variables. The talk will review results by F. Cucker, P. Koiran and S. Smale, 1999, H.J. Lenstra (Jr.), 1999, E. Kaltofen and P. Koiran, 2005 and 2006, and a joint work with M. Avendaño and M. Sombra, 2006.