We present CIRCLE, a framework for large-scale scene completion and geometric refinement based on local implicit signed distance functions. It is based on an end-to-end sparse convolutional network, CircNet, that jointly models local geometric details and global scene structural contexts, allowing it to preserve fine-grained object detail while recovering missing regions commonly arising in traditional 3D scene data. A novel differentiable rendering module enables test-time refinement for better reconstruction quality. Extensive experiments on both real-world and synthetic datasets show that our concise framework is efficient and effective, achieving better reconstruction quality than the closest competitor while being 10-50x faster.