Since the 1980s, the main approach to automatic speech recognition has been using hidden Markov models (HMMs), in which each state corresponds to a phoneme or part of a phoneme in the context of the neighboring phonemes. Despite their crude approximation of the speech signal, and the large margin for improvement still remaining, HMMs have proven difficult to beat. In the last few years, there has been increasing interest in more complex graphical models for speech recognition, involving multiple streams of states. I will describe two such approaches, one modeling pronunciation variation as the result of the "sloppy" behavior of articulatory variables (the states of the lips, tongue, etc.) and the other modeling the audio and visual states in audio-visual speech recognition (i.e. recognition enhanced by "lipreading").