Recurrent neural network training in Python (RectiPy) is a software package developed by Richard Gast that allows for lightweight implementations of recurrent neural networks (RNNs) based on ordinary or delayed differential equations. The main purpose of the software is to provide a tool that allows for the implementation of biologically informed spiking neural networks and optimize the parameters of these networks via gradient descent. As such, RectiPy can be used to optimize a spiking network model of the basal ganglia to fit neural activity recordings, for example. RectiPy provides an intuitive YAML interface for model definition, and leverages PyRates to translate these model definitions into PyTorch functions. This way, users can easily define their own neuron models, spike-based or rate-based, and use them to create a RNN model. All model training, testing, as well as numerical integration of the differential equations is also performed in PyTorch. Thus, RectiPy comes with all the gradient-based optimization and parallelization features that PyTorch provides. RectiPy is freely available at https://github.com/pyrates-neuroscience/RectiPy and comes with a full online documentation and various use examples: