BPE (Byte-Pair Encoding) is a tokenization algorithm that builds vocabulary by iteratively merging the most frequent character pairs. Algorithm: Start with character vocabulary, count all adjacent pair frequencies, merge most frequent pair into new token, repeat until vocabulary size reached. Example: The word lowest might tokenize as low + est if those subwords are in vocabulary. Training: Run on corpus, learn merge operations, store merge rules for encoding new text. Inference: Apply learned merges greedily to tokenize new text. Advantages: Handles rare words (split into subwords), no OOV, compact vocabulary, language-agnostic. Used by: GPT-2, GPT-3, GPT-4 (with byte-level variant), RoBERTa. Variants: Byte-level BPE (operates on bytes, handles any Unicode), BPE with dropout (regularization). Comparison: WordPiece uses likelihood-based selection, Unigram uses probabilistic model. Trade-offs: Vocabulary size affects sequence length and model size. Implementation: tiktoken (OpenAI), tokenizers library (HuggingFace). Foundational algorithm for modern LLM tokenization.