Stories and narratives are composed based on a variety of events. Understanding how these events are semantically related to each other is the essence of reading comprehension. Recent event-centric reading comprehension datasets focus on either event arguments or event temporal commonsense. Although these tasks evaluate machines' ability of narrative understanding, human-like reading comprehension requires the capability to process event-based semantics beyond arguments and temporal commonsense. For example, to understand causality between events, we need to infer motivations or purposes; to understand event hierarchy, we need to parse the composition of events. To facilitate these tasks, we introduce ESTER, a comprehensive machine reading comprehension (MRC) dataset for Event Semantic Relation Reasoning. We study the five most commonly used event semantic relations and formulate them as question answering tasks. Experimental results show that the current SOTA systems achieve 60.5%, 57.8%, and 76.3% for event-based F1, token-based F1, and HIT@1 scores respectively, which are significantly below human performances.