This report provides the first estimates of the genetic basis of all key breast muscle myopathies (BMM) in broiler chickens [Deep pectoral myopathy, wooden breast, white striping and spaghetti breast] and their relationship with body weight and breast yield. Data from a pure bred high yielding commercial broiler line were analysed to estimate the genetic parameters using a multivariate animal model with the appropriate fixed effects and permanent environmental effect of the dam. Heritabilities of the BMM ranged from 0.04 to 0.25 and the genetic correlation of the BMM with body weight and breast yield ranged from -0.06 to 0.41. Here we highlight that the genetic variance of BMM accounts for a low proportion of the phenotypic variance and the BMM have a low genetic relationship with performance traits. The large contribution of residual variance to the phenotypic variance for the BBM was >71.5% which indicates the importance of the non-genetic effects on BMM. The data presented also show that the moderate to low genetic influence for the development of BMM can be used, through balanced selection, to reduce the myopathy incidence in the long term. The impact of genetic selection against BMM was tested empirically by comparing the incidence of WB and % breast yield of a commercial broiler with a high generation (HG) broiler. The HG broiler used represents 2 years of genetic improvement compared to the commercial broiler; the HG broiler had an 18.4% relative decrease in WB and a 1.02% relative increase in breast yield compared to the commercial broiler. This paper describes the relationship between the genetic and non-genetic factors influencing BMM highlighting the importance of understanding the non-genetic effects on myopathy incidence. It also shows that the genetic component of BMM can be reduced whilst at the same time improving breast yield as part of balanced breeding goals.