There is considerable interest in projections of future productivity growth in agriculture. Whether one is interested in the outlook for global commodity markets, future patterns of international trade, or the interactions between land use, deforestation and ecological diversity, the rate of productivity growth in agriculture is an essential input. Yet solid projections for this variable have proven elusive - particularly on a global basis. This is due, in no small part, to the difficulty in measuring historical productivity growth. The purpose of this paper is to report the latest time series evidence on total factor productivity growth for crops, ruminants and non-ruminant livestock, on a global basis. We then follow with tests for convergence amongst regions, providing forecasts for farm productivity growth to the year 2040. The results suggest that most regions in the sample are likely to experience larger productivity gains in livestock than in crops. Within livestock, the non-ruminant sector is expected to continue to be more dynamic than the ruminant sector. Given the rapid rates of productivity growth observed recently, non-ruminant and crop productivity in developing countries may be converging to the productivity levels of developed countries. For ruminants, the results show that productivity levels may be diverging between developed and developing countries.