Autonomous agents that sense, reason, and act in real-world environments for extended periods often need to solve streams of incoming problems. Traditionally, effort is applied only to problems that have already arrived and have been noted. We examine continual computation methods that allow agents to ideally allocate time to solving current as well as potential future problems under uncertainty. We first review prior work on continual computation. Then, we present new directions and results, including the consideration of shared subtasks and multiple tasks. We present results on the computational complexity of the continual-computation problem and provide approximations for arbitrary models of computational performance. Finally, we review special formulations for addressing uncertainty about the best algorithm to apply, learning about performance, and considering costs associated with delayed use of results.