In this paper, we present an Efficient Planning System for automated vehicles In highLy interactive envirONments (EPSILON). EPSILON is an efficient interaction-aware planning system for automated driving, and is extensively validated in both simulation and real-world dense city traffic. It follows a hierarchical structure with an interactive behavior planning layer and an optimization-based motion planning layer. The behavior planning is formulated from a partially observable Markov decision process (POMDP), but is much more efficient than naively applying a POMDP to the decision-making problem. The key to efficiency is guided branching in both the action space and observation space, which decomposes the original problem into a limited number of closed-loop policy evaluations. Moreover, we introduce a new driver model with a safety mechanism to overcome the risk induced by the potential imperfectness of prior knowledge. For motion planning, we employ a spatio-temporal semantic corridor (SSC) to model the constraints posed by complex driving environments in a unified way. Based on the SSC, a safe and smooth trajectory is optimized, complying with the decision provided by the behavior planner. We validate our planning system in both simulations and real-world dense traffic, and the experimental results show that our EPSILON achieves human-like driving behaviors in highly interactive traffic flow smoothly and safely without being over-conservative compared to the existing planning methods.