This presentation, delivered as part of the 2025 1st Workshop on Grid Connected Converters, focuses on advanced control and stability aspects of microgrids integrating grid-forming (GFM) and grid-following (GFL) power converters. With the rapid expansion of renewable energy sources, modern power networks are evolving from synchronous-machine-based systems toward converter-dominated grids, leading to new challenges in dynamic performance, synchronization, and fault response. The session covers the fundamental operating principles of GFM and GFL converters, hierarchical control structures (primary, secondary, and tertiary levels), and synchronization mechanisms under weak-grid conditions. Advanced topics include inertia emulation, droop-based control, virtual synchronous machine (VSM) strategies, and fault ride-through (FRT) enhancement. Through simulation demonstrations and practical case studies, the workshop highlights effective design principles for robust and resilient converter-based microgrids suited to next-generation smart power systems.