This book is intended to give an overview of the major results achieved in the field of natural speech understanding inside ESPRIT Project P. 26, "Advanced Algorithms and Architectures for Speech and Image Processing". The project began as a Pilot Project in the early stage of Phase 1 of the ESPRIT Program launched by the Commission of the European Communities. After one year, in the light of the preliminary results that were obtained, it was confirmed for its 5-year duration. Even though the activities were carried out for both speech and image understanding we preferred to focus the treatment of the book on the first area which crystallized mainly around the CSELT team, with the valuable cooperation of AEG, Thomson-CSF, and Politecnico di Torino. Due to the work of the five years of the project, the Consortium was able to develop an actual and complete understanding system that goes from a continuously spoken natural language sentence to its meaning and the consequent access to a database. When we started in 1983 we had some expertise in small-vocabulary syntax-driven connected-word speech recognition using Hidden Markov Models, in written natural language understanding, and in hardware design mainly based upon bit-slice microprocessors.