Some extensions of neoclassical growth models are discussed that allow for cross section heterogeneity among economies and evolution in rates of technological progress over time. The models offer a spectrum of transitional behavior among economies that includes convergence to a common steady state path as well as various forms of transitional divergence and convergence. Mechanisms for modeling such transitions and measuring them econometrically are developed in the paper. A new regression test of convergence is proposed, its asymptotic properties are derived and some simulations of its finite sample properties are reported. Transition curves for individual economies and subgroups of economies are estimated in a series of empirical applications of the methods to regional US data, OECD data and Penn World Table data.