Network slicing means an emerging business to operators and allows them to sell the customized slices to various tenants at different prices. In order to provide better-performing and costefficient services, network slicing involves challenging technical issues and urgently looks forward to intelligent innovations to make the resource management consistent with users' activities per slice. In that regard, deep reinforcement learning (DRL), which focuses on how to interact with the environment by trying alternative actions and reinforces the tendency actions producing more rewarding consequences, is emerging as a promising solution. In this paper, after briefly reviewing the fundamental concepts and evolution-driving factors of DRL, we investigate the application of DRL in some typical resource management scenarios of network slicing, which include radio resource slicing and priority-based core network slicing, and demonstrate the performance advantage of DRL over several competing schemes through extensive simulations. Finally, we also discuss the possible challenges to apply DRL in network slicing from a general perspective.