Make-A-Shape is a novel 3D generative model designed to efficiently train on massive datasets. It leverages 10 million publicly available shapes. We innovatively introduce a wavelet tree representation, encoding shapes compactly via a subband coefficient filtering scheme. Subband coefficients are then packaged and arranged on a low-resolution mesh to enable diffusion model generation. Furthermore, we propose a subband adaptive training strategy, allowing our model to effectively learn the generation of coarse-to-fine wavelet coefficients. Finally, we extend our framework to be controlled by additional input conditions, enabling shape generation from various modalities, including single/multi-view images, point clouds, and low-resolution voxels. Extensive experiments demonstrate the efficacy of our method in various applications, including unconditional generation, shape completion, and conditional generation. Our approach not only surpasses existing techniques in providing high-quality results but also efficiently generates shapes in seconds, typically requiring only 2 seconds under most conditions.