Process mining combines traditional process analysis with data-centric techniques to improve performance and ensure compliance in organizations. It focuses on discovering process models from real event logs and checking for discrepancies between models and actual behavior. By aligning and comparing modeled and observed behavior, conformance checking techniques enrich process models with performance information. This tutorial paper explores process discovery and conformance checking techniques, highlighting algorithmic challenges in process mining and its potential for advancing research on concurrency models like Petri nets.