A query became slow in production. How do you investigate?

Confirm and measure: which query, how slow, since when (slow query log, pg_stat_statements, APM traces).
Reproduce with EXPLAIN ANALYZE; look for sequential scans, wrong row estimates, expensive sorts, nested loops over big sets.
Check recent changes: deploys, data growth, new filters, outdated statistics (ANALYZE).
Fixes: add or adjust indexes (composite, covering, partial), rewrite the query, avoid N+1, paginate, cache, denormalize or add a read replica.
Check locks and connection pool saturation.
Verify the fix with the same measurement and add monitoring.