Explain LSM Trees and why they are used in write-optimized databases.

Log-Structured Merge Trees optimize write-heavy workloads by converting random writes to sequential writes. Writes go to an in-memory buffer (memtable); when full, it flushes to disk as sorted immutable file (SSTable). Background compaction merges SSTables. Reads check memtable then SSTables (aided by bloom filters). Writes are O(1) amortized, reads are slower than B-trees but acceptable with optimizations. Used in LevelDB, RocksDB, Cassandra, and HBase.