Artificial Neural Networks (ANNs) trained on specific cognitive tasks have re-emerged as a useful tool to study the brain. However, ANNs would better aid cognitive neuroscience if a given network could be easily trained on a wide range of tasks for which neural recordings are available. Moreover, unintentional divergent implementations of cognitive tasks can produce variable results, which limits their interpretability. Towards this goal, we present NeuroGym, an open-source Python package that provides a large collection of customizable neuroscience tasks to test and compare network models. Building upon the OpenAI Gym toolbox, NeuroGym tasks (1) are written in a high-level flexible Python framework;(2) possess a shared interface tailored to common needs of neuroscience tasks that facilitates their design and usage;(3) support the training of ANNs using both Reinforcement and Supervised Learning techniques. The toolbox allows easy assembly of new tasks by modifying existing ones in a hierarchical and modular fashion. These design features make it straightforward to take a network designed for one task and train it on many other tasks. NeuroGym is a community-driven effort that contributes to a rapidly evolving open ecosystem of neural network development, data analysis, and model-data comparison.