We propose a set of environments with dynamic tasks that involve highly deformable topologically non-trivial objects. These environments facilitate easy experimentation: offer fast runtime, support large-scale parallel data generation, are easy to connect to reinforcement learning frameworks with OpenAI Gym API. We offer several types of benchmark tasks with varying levels of complexity, provide variants with procedurally generated cloth objects and randomized material textures. Moreover, we allow users to customize the tasks: import custom objects and textures, adjust size and material properties of deformable objects. We prioritize dynamic aspects of the tasks: forgoing 2D tabletop manipulation in favor of 3D tasks, with gravity and inertia playing a non-negligible role. Such advanced challenges require insights from multiple fields: machine learning and computer vision to process high-dimensional inputs, methods from computer graphics and topology to inspire structured and interpretable representations, insights from robotics to learn advanced control policies. We aim to help researches from these fields contribute their insights and simplify establishing interdisciplinary collaborations.