Quantitative genetics provides a theoretical framework that can be used to relate information on the inheritance and heritability of traits to predictions of selection response for a breeding program. These prediction equations are constructed under a number of simplifying assumptions regarding the genetic architecture of the traits. Recent studies, using molecular techniques have emphasized that a breeder is likely to encounter traits under forms of genetic control that range from simple to complex. A quantitative understanding of the relationships between the complexity of the genetic control of trait variation and the effectiveness of breeding strategies is required. Presently we have at best only a qualitative understanding of these relationships. The theoretical framework for quantitative genetics is progressing more slowly than is the accumulation of experimental information on the genetic architecture of traits. We are using computer simulation to overcome some of the difficulties associated with the conventional approach for developing theoretical prediction equations. Ultimately this should direct us to appropriate pathways for advancing the theoretical framework. In the meantime there are considerable opportunities to use computer simulation to answer questions relating to improving the efficiency of current breeding strategies.