We propose a unified methodology to analyze the performance of caches (both isolated and interconnected), by extending and generalizing a decoupling technique originally known as Che’s approximation, which provides very accurate results at low computational cost. We consider several caching policies (including a very attractive one, called k-LRU), taking into account the effects of temporal locality. In the case of interconnected caches, our approach allows us to do better than the Poisson approximation commonly adopted in prior work. Our results, validated against simulations and trace-driven experiments, provide interesting insights into the performance of caching systems.