Neither traditional disk-based database systems nor modern inmemory database systems are capable of fully exploiting modern servers with multiple NVMe SSDs. LeanStore is a high-performance OLTP storage engine specifically optimized for NVMe SSDs and multi-core CPUs. The paper gives an overview of the architecture of LeanStore and describes all major components, covering caching, page replacement, I/O management, indexing, data structure synchronization, multi-version concurrency control, logging, checkpoints, and recovery. We also discuss some of the low-level implementation techniques necessary for achieving high performance on modern hardware.