We present Voice Activity Projection (VAP), a model trained on spontaneous spoken dialog with the objective to incrementally predict future voice activity. Similar to a language model, it is trained through self-supervised learning and outputs a probability distribution over discrete states that corresponds to the joint future voice activity of the dialog interlocutors. The model is well-defined over overlapping speech regions, resilient towards microphone “bleed-over” and considers the speech of both speakers (e.g., a user and an agent) to provide the most likely next speaker. VAP is a general turn-taking model which can serve as the base for turn-taking decisions in spoken dialog systems, an automatic tool useful for linguistics and conversational analysis, an automatic evaluation metric for conversational text-to-speech models, and possibly many other tasks related to spoken dialog interaction.