There isn't a one-size-fits all approach, but I've never worked on a project that encompasses as many computer science algorithms as a search engine.
- Tries (patricia, radix, etc...)
- Trees (b-trees, b+trees, merkle trees, log-structured merge-tree, etc..)
- Consensus (raft, paxos, etc..)
- Block storage (disk block size optimizations, mmap files, delta storage, etc..)
- Probabilistic filters (hyperloloog, bloom filters, etc...)
- Binary Search (sstables, sorted inverted indexes)
- Ranking (pagerank, tf/idf, bm25, etc...)
- NLP (stemming, POS tagging, subject identification, etc...)
- HTML (document parsing/lexing)
- Images (exif extraction, removal, resizing / proxying, etc...)
- Queues (SQS, NATS, Apollo, etc...)
- Clustering (k-means, density, hierarchical, gaussian distributions, etc...)
- Rate limiting (leaky bucket, windowed, etc...)
- text processing (unicode-normalization, slugify, sanitation, lossless and lossy hashing like metaphone and document fingerprinting)
- etc...
I'm sure there is plenty more I've missed. There are lots of generic structures involved like hashes, linked-lists, skip-lists, heaps and priority queues and this is just to get 2000's level basic tech.
- https://github.com/quickwit-oss/tantivy
- https://github.com/valeriansaliou/sonic
- https://github.com/mosuka/phalanx
- https://github.com/meilisearch/MeiliSearch
- https://github.com/blevesearch/bleve
- https://github.com/thomasjungblut/go-sstables
A lot of people new to this space mistakenly think you can just throw elastic search or postgres fulltext search in front of terabytes of records and have something decent. That might work for something small like a curated collection of a few hundred sites.