Part 4 of a series on PostgreSQL indexing covers three extension-based index types available in Amazon Aurora PostgreSQL and RDS for PostgreSQL. Bloom indexes use probabilistic filters for space-efficient multi-column equality filtering, replacing multiple B-tree indexes with a single lossy index. pg_trgm breaks text into trigrams to enable fuzzy matching, similarity searches, and LIKE/ILIKE pattern matching via GIN or GiST indexes, with tunable similarity thresholds. pg_bigm uses bigrams (2-character sequences) for full-text search in Asian languages like Japanese, Chinese, and Korean that lack whitespace word delimiters. Each extension's use cases, tuning parameters, performance characteristics, and limitations are covered with SQL examples.