Mapping behavioural actions to neural activity is a fundamental goal of neuroscience. As our ability to record large neural and behavioural data increases, there is growing interest in modelling neural dynamics during adaptive behaviours to probe neural representations(1-3). In particular, although neural latent embeddings can reveal underlying correlates of behaviour, we lack nonlinear techniques that can explicitly and flexibly leverage joint behaviour and neural data to uncover neural dynamics(3-5). Here, we fill this gap with a new encoding method, CEBRA, that jointly uses behavioural and neural data in a (supervised) hypothesis- or (self-supervised) discovery-driven manner to produce both consistent and high-performance latent spaces. We show that consistency can be used as a metric for uncovering meaningful differences, and the inferred latents can be used for decoding. We validate its accuracy and demonstrate our tool's utility for both calcium and electrophysiology datasets, across sensory and motor tasks and in simple or complex behaviours across species. It allows leverage of single- and multi-session datasets for hypothesis testing or can be used label free. Lastly, we show that CEBRA can be used for the mapping of space, uncovering complex kinematic features, for the production of consistent latent spaces across two-photon and Neuropixels data, and can provide rapid, high-accuracy decoding of natural videos from visual cortex.