Automatic speech recognition (ASR) systems based on hidden Markov models (HMMs) are effective under many circumstances, but do suffer from some major limitations that limit their applicability in real-world environments. In particular, the 'local stationarity' requirement, implicit in standard HMMs, appears to be constraining. This paper reviews the major concepts underlying HMMs for ASR, pointing out a number of alternatives to enhance the basic paradigm in order to overcome the local-stationarity problem. Alternatives considered herein are: (i) introduction of dynamic acoustic features; (ii) definition of contest-dependent acoustic units; (iii) integration of segmental information; (iv) combination of artificial neural networks within hybrid HMM/connectionist architectures