This paper develops a model of the optimal investment strategy for a firm confronted with a sequence of technological innovations. We incorporate many of the most important characteristics of real-world technology markets. For example, we permit innovations to be stochastic in their arrival times and their profitability. We also incorporate learning so that firms adopting current innovations become better able to benefit from future innovations. The model yields four distinct investment strategies. The model is then used to predict actual firm policy. These implications are discussed and compared with observed firm behavior.