Neural firing rates in the macaque lateral intraparietal (LIP) cortex exhibit gradual "ramping" that is commonly believed to reflect the accumulation of sensory evidence during decision-making. However, ramping that appears in trial-averaged responses does not necessarily indicate that the spike rate ramps on single trials; a ramping average rate could also arise from instantaneous steps that occur at different times on each trial. In this talk, I will describe an approach to this problem based on explicit statistical latent-dynamical models of spike trains. We analyzed LIP spike responses using spike train models with: (1) ramping "accumulation-to-bound" dynamics; and (2) discrete "stepping" or "switching" dynamics. Surprisingly, we found that a majority of choice-selective neurons in LIP are better explained by a model with stepping dynamics. We show that the stepping model provides an accurate description of LIP spike trains, allows for accurate decoding of decisions, and reveals latent structure that is hidden by conventional stimulus-aligned analyses. Finally, I will discuss more recent insights into the coding of decisions using simultaneous multi-neuron recording in areas MT and LIP during decision formation.