The weighted ensemble (WE) method is an enhanced sampling strategy based on periodically replicating and pruning trajectories generated in parallel. WE has grown increasingly popular for computational biochemistry problems, due in part to improved hardware and accessible software implementations. Algorithmic and analytical improvements have also played an important role, and progress has accelerated in recent years.Here, we discuss and elaborate on the WE method from a mathematical perspective, highlighting recent results which enhance the computational efficiency.The mathematical theory reveals a new strategy for optimizing trajectory management that approaches the best possible variance while generalizing to systems of arbitrary dimension.