We present fVDB, a novel GPU-optimized framework for deep learning on large-scale 3D data. fVDB provides a complete set of differentiable primitives to build deep learning architectures for common tasks in 3D learning such as convolution, pooling, attention, ray-tracing, meshing, etc. fVDB simultaneously provides a much larger feature set (primitives and operators) than established frameworks with no loss in efficiency: our operators match or exceed the performance of other frameworks with narrower scope. Furthermore, fVDB can process datasets with much larger footprint and spatial resolution than prior works, while providing a competitive memory footprint on small inputs. To achieve this combination of versatility and performance, fVDB relies on a single novel VDB index grid acceleration structure paired with several key innovations including GPU accelerated sparse grid construction, convolution using tensorcores, fast ray tracing kernels using a Hierarchical Digital Differential Analyzer algorithm (HDDA), and jagged tensors. Our framework is fully integrated with PyTorch enabling interoperability with existing pipelines, and we demonstrate its effectiveness on a number of representative tasks such as large-scale point-cloud segmentation, high resolution 3D generative modeling, unbounded scale Neural Radiance Fields, and large-scale point cloud reconstruction.