MPII Human Shape is a family of expressive 3D human body shape models and tools for human shape space building, manipulation and evaluation. Human shape spaces are based on the widely used statistical body representation and learned from the CAESAR dataset, the largest commercially available scan database to date. As preprocessing several thousand scans for learning the models is a challenge in itself, we contribute by developing robust best practice solutions for scan alignment that quantitatively lead to the best learned models. We make the models as well as the tools publicly available. Extensive evaluation shows improved accuracy and generality of our new models, as well as superior performance for human body reconstruction from sparse input data.