As process mining gains traction as a tool for analyzing and improving processes in the industry as exemplified by companies such as Disco, Celonis, and Minit, many commercial process mining tools are extending beyond process discovery to include conformance checking features. Performing conformance checking in industrial settings means that techniques have to be functional with industrial sized processes and real-life settings. In this thesis, we propose three approaches: a divide-and-conquer approach to alignment, conformance checking algorithm selection and a HMM-based approach to online conformance checking.