Time series models are ubiquitous in science, arising in any situation where researchers seek to understand how a system’s behaviour changes over time. A key problem in time series modelling is inference; determining properties of the underlying system based on observed time series. For both statistical and mechanistic models, inference involves finding parameter values, or distributions of parameters values, which produce outputs consistent with observations. A wide variety of inference techniques are available and different approaches are suitable for different classes of problems. This variety presents a challenge for researchers, who may not have the resources or expertise to implement and experiment with these methods. PINTS (Probabilistic Inference on Noisy Time Series — https://github.com/pints-team/pints) is an open-source (BSD 3-clause license) Python library that provides researchers with a broad suite of non-linear optimisation and sampling methods. It allows users to wrap a model and data in a transparent and straightforward interface, which can then be used with custom or pre-defined error measures for optimisation, or with likelihood functions for Bayesian inference or maximum-likelihood estimation. Derivative-free optimisation algorithms — which work without harder-to-obtain gradient information — are included, as well as inference algorithms such as adaptive Markov chain Monte Carlo and nested sampling, which estimate distributions over parameter values. By making these statistical techniques available in an open and easy-to-use framework, PINTS brings the power of these modern methods to a wider scientific audience. Funding statement: M.C., G.R.M. and D.J.G. acknowledge support from the UK Biotechnology and Biological Sciences Research Council [BBSRC grant number BB/P010008/1]; M.R., S.G. and D.J.G. gratefully acknowledge research support from the UK Engineering and Physical Sciences Research Council Cross-Disciplinary Interface Programme [EPSRC grant number EP/I017909/1]; C.L.L. acknowledges support from the Clarendon Scholarship Fund, the EPSRC and the UK Medical Research Council (MRC) [EPSRC grant number EP/L016044/1]; B.L. acknowledges support from the UK Engineering and Physical Sciences Research Council [EPSRC grant number EP/F500394/1]; and S.G. and G.R.M. acknowledge support from the Wellcome Trust & Royal Society [Wellcome Trust grant numbers 101222/Z/13/Z and 212203/Z/18/Z].