AbstractThis chapter asks: How can evolutionary potential be measured? The question is deceptively simple: whilst evolutionary potential is typically defined on a per-trait basis, it has become clear that the complex genetic architecture of quantitative traits requires other ways to quantify evolutionary potential and constraints. This chapter reviews knowledge about multivariate evolutionary potential in the wild and the extent to which genetic covariances, as summarized in the G-matrix, impact evolutionary trajectories of natural populations both in terms of rate and direction. In terms of constraints, genetic covariances among traits can slow down the rate of adaptation, and influence the direction of the response to selection. However, the constraints posed by genetic covariances are insurmountable only if G-matrices are stable. The chapter thus reviews firstly theoretical predictions about the stability of G in relation to selection, migration and drift, and secondly methods available to test differentiation among matrices. To date, a majority of studies imply conservatism of G-matrices; however, a couple of recent studies have revealed that differentiation of G-matrices among wild populations can also be very fast, especially during colonisation of new habitats. Furthermore, as an increasing number of methods have been proposed for comparing G-matrices, we assessed how these methods perform under different hypothetical scenarios. The chapter shows that limited statistical power could often lead to erroneous conclusion of matrix conservatism, suggesting caution is needed in interpreting the results of matrix comparisons. The chapter concludes by identifying areas in need of further research.