This paper discusses some of the recent developments in growth theory, doing so from the perspective of a small open economy. After setting out a basic generic model, we show how it may yield two of the key models that have played a prominent role in the recent literature, the endogenous growth model and the non-scale growth model. We focus initially on the former, emphasizing how the simplest such model leads to an equilibrium in which the economy is always on its balanced growth path. One aspect of the model is the importance of fiscal policy as a determinant of the equilibrium growth rate, an aspect that is discussed in detail. We also show how the endogeneity or otherwise of the labor supply is crucial in determining the equilibrium growth rate and its responsiveness to macroeconomic policy. But transitional dynamics are an important aspect of the growth process and indeed much research has been directed to determining the speed with which the economy converges to its balanced growth path. We discuss alternative ways that such transitional dynamics may be introduced. These include (i) restricted access to the world capital market; (ii) the introduction of government capital , and (iii) the two-sector production model, pioneered by Lucas. In the original analysis, the two capital goods relate to physical and human capital and in the international context these naturally can be identified with traded and nontraded capital, respectively. Criticism of the endogenous growth model has led to the development of the nonscale growth model. This too is characterized by transitional dynamics, which are more flexible than those of the corresponding endogenous growth model. This model is much closer to the neoclassical model; in particular, the long-run growth rate is independent of macroeconomic policy. However, since such models are typically associated with slow convergence speeds, policy can influence the accumulation of capital for extended periods of time, leading to significant long-run level effects. The discussion seeks to emphasize the adaptability of the models to a wide range of issues. A final extension addresses the impact of volatililty on growth. This has been extensively analyzed empirically and a stochastic extension of the endogenous growth model provides a convenient framework within which to interpret this research.