Sequential neuronal activity underlies a wide range of processes in the brain. Neuroscientific evidence for neuronal sequences has been reported in domains as diverse as perception, motor control, speech, spatial navigation and memory. Consequently, different dynamical principles have been proposed as possible sequence-generating mechanisms. Combining experimental findings with computational concepts like the Bayesian brain hypothesis and predictive coding leads to the interesting possibility that predictive and inferential processes in the brain are grounded on generative processes which maintain a sequential structure. While probabilistic inference about ongoing sequences is a useful computational model for both the analysis of neuroscientific data and a wide range of problems in artificial recognition and motor control, research on the subject is relatively scarce and distributed over different fields in the neurosciences. Here we review key findings about neuronal sequences and relate these to the concept of online inference on sequences as a model of sensory-motor processing and recognition. We propose that describing sequential neuronal activity as an expression of probabilistic inference over sequences may lead to novel perspectives on brain function. Importantly, it is promising to translate the key idea of probabilistic inference on sequences to machine learning, in order to address challenges in the real-time recognition of speech and human motion.