GPU computing is becoming increasingly more popular with the proliferation of deep learning (DL) applications. However, unlike traditional resources such as CPU or the network, modern GPUs do not natively support fine-grained sharing primitives. Consequently, implementing common policies such as time sharing and preemption are expensive. Worse, when a DL application cannot completely use a GPU's resources, the GPU cannot be efficiently shared between multiple applications, leading to GPU underutilization. We present Salus to enable two GPU sharing primitives: fast job switching and memory sharing, in order to achieve fine-grained GPU sharing among multiple DL applications. Salus implements an efficient, consolidated execution service that exposes the GPU to different DL applications, and enforces fine-grained sharing by performing iteration scheduling and addressing associated memory management issues. We show that these primitives can then be used to implement flexible sharing policies such as fairness, prioritization, and packing for various use cases. Our integration of Salus with TensorFlow and evaluation on popular DL jobs show that Salus can improve the average completion time of DL training jobs by $3.19\times$, GPU utilization for hyper-parameter tuning by $2.38\times$, and GPU utilization of DL inference applications by $42\times$ over not sharing the GPU and $7\times$ over NVIDIA MPS with small overhead.