An exponential growth of event data can be witnessed across all industries. Devices connected to the internet (internet of things), social interaction, mobile computing, and cloud computing provide new sources of event data and this trend will continue. The omnipresence of large amounts of event data is an important enabler for process mining. Process mining techniques can be used to discover, monitor and improve real processes by extracting knowledge from observed behavior. However, unprecedented volumes of event data also provide new challenges and often state-of-the-art process mining techniques cannot cope. This paper focuses on "conformance checking in the large" and presents a novel decomposition technique that partitions larger process models and event logs into smaller parts that can be analyzed independently. The so-called Single-Entry Single-Exit (SESE) decomposition not only helps to speed up conformance checking, but also provides improved diagnostics. The analyst can zoom in on the problematic parts of the process. Importantly, the conditions under which the conformance of the whole can be assessed by verifying the conformance of the SESE parts are described, which enables the decomposition and distribution of large conformance checking problems. All the techniques have been implemented in ProM, and experimental results are provided.