For an introduction, see Wikipedia - Beam Search.

• Beam search for RNNs: Rush et al 2015 - A Neural Attention Model for Abstractive Sentence Summarization This may be the first paper to use beam search in seq2seq models (as far as Jeff knows)

Invented for decoding in speech recognition, beam search was the de-facto decoding algorithm for statistical machine translation and was also used for statistical parsing. Historical references are here:

• Speech Recognition
  • Jelinek 1969 - Fast Sequential Decoding Algorithm Using a Stack This is the standard stack-based beam search decoder, used extensively in statistical MT. Cited and used by Brown et al 1988 for MT. Didn't use the term beam search however.
• Machine translation, see Statistical Machine Translation
  • Och et al 2003 - Statistical Phrase-Based Translation
  • Khoen 2004 - Pharaoh: a beam search decoder for phrase-based statistical machine translation models

• Decoding
• Seq2seq