Neural receptive fields are dynamic in that with experience, neurons change their spiking responses to relevant stimuli. To understand how neural systems adapt their representations of biological information, analyses of receptive field plasticity from experimental measurements are crucial. Adaptive signal processing, the well-established engineering discipline for characterizing the temporal evolution of system parameters, suggests a framework for studying the plasticity of receptive fields. We use the Bayes' rule Chapman-Kolmogorov paradigm with a linear state equation and point process observation models to derive adaptive filters appropriate for estimation from neural spike trains. We derive point process filter analogues of the Kalman filter, recursive least squares, and steepest-descent algorithms and describe the properties of these new filters. We illustrate our algorithms in two simulated data examples. The first is a study of slow and rapid evolution of spatial receptive fields in hippocampal neurons. The second is an adaptive decoding study in which a signal is decoded from ensemble neural spiking activity as the receptive fields of the neurons in the ensemble evolve. Our results provide a paradigm for adaptive estimation for point process observations and suggest a practical approach for constructing filtering algorithms to track neural receptive field dynamics on a millisecond timescale.