refnx is a model-based neutron and X-ray reflectometry data analysis package written in Python. It is cross platform, and has been tested on Linux, macOS, and Windows. Its graphical user interface is browser-based, through a Jupyter notebook. Model construction is modular, being composed from a series of components that each describe a subset of the interface, parameterised in terms of physically relevant parameters (volume fraction of a polymer, lipid area per molecule, etc). The model and data are used to create an objective, which is used to calculate residuals, log-likelihood, and log-prior probabilities of the system. Objectives are combined to perform co-refinement of multiple datasets, and mixed-area models. Prior knowledge of parameter values is encoded as probability distribution functions or bounds on all parameters in the system. Additional prior probability terms can be defined for sets of components, over and above those available from the parameters alone. Algebraic parameter constraints are available. A choice of fitting approaches is available, including least-squares (global and gradient-based optimizers) and a Bayesian approach using Markov Chain Monte Carlo to investigate the posterior distribution of the model parameters. The Bayesian approach is useful in examining parameter covariances, model selection, and variability in the resulting scattering length density profiles. The package is designed to facilitate reproducible research; its use in Jupyter notebooks, and subsequent distribution of those notebooks as supporting information, permits straightforward reproduction of analyses.