Time structures ecological communities. The strength and outcomes of species interactions are often determined by the temporal sequence and interval of species arrival, a phenomenon termed priority effects. As climate change shifts species timing (phenology) worldwide, we need a general theoretical framework to understand the diverse biological mechanisms underlying priority effects and their consequences in various communities. I first propose a general categorization of priority effects based on their biological mechanisms and the time scales at which they operate. With simulation and experiments of two species communities, I show that the importance of the two categories of mechanisms depends on relative scales between differences in arrival times and the length of the life cycles. Scaling up, I show that how biodiversity changes with dispersal in spatially structured, multispecies communities is also determined by the category of priority effects. Finally, I extend priority effects beyond pairwise interaction with a three-species mechanistic model of plant-soil feedback and propose a general framework to quantify such time-dependent interaction modifications. Together, these works provide a new direction in studying temporal processes in complex communities.