gallifrey performs Bayesian structure learning and inference with Gaussian Process (GP) models for time-series data. It enables efficient construction, evaluation, and analysis of GP models and supports exploration of model structure within a probabilistic framework. The package utilizes JAX for efficient numerical computation and Sequential Monte Carlo (SMC) methods for robust posterior approximation. Unlike most Gaussian Process packages, where a covariance function needs to be specified explicitly, the code infers the covariance structure from the time series. gallifrey was created with exoplanet transit light curves in mind, but is applicable to a wide variety of time series modelling, analysis, and forecasting tasks.