The local study of elliptic curves modulo primes is one of the most powerful tools, both conjecturally and actually, for proving global results. The trace of the Frobenius morphism is a measure of how far an elliptic curve departs from its expected local behavior, and Lang and Trotter have a well-known conjecture regarding the distribution of these traces for a given curve. In this talk we will discuss some results related to this conjecture for certain families of elliptic curves.