We present Neural Strands, a novel learning framework for modeling accurate hair geometry and appearance from multi-view image inputs. The learned hair model can be rendered in real-time from any viewpoint with high-fidelity view-dependent effects. Our model achieves intuitive shape and style control unlike volumetric counterparts. To enable these properties, we propose a novel hair representation based on a neural scalp texture that encodes the geometry and appearance of individual strands at each texel location. Furthermore, we introduce a novel neural rendering framework based on rasterization of the learned hair strands. Our neural rendering is strand-accurate and anti-aliased, making the rendering view-consistent and photorealistic. Combining appearance with a multi-view geometric prior, we enable, for the first time, the joint learning of appearance and explicit hair geometry from a multi-view setup. We demonstrate the efficacy of our approach in terms of fidelity and efficiency for various hairstyles.