Event is a common but non-negligible knowledge type. How to identify events from texts, extract their arguments, even analyze the relations between different events are important for many applications. This paper summaries some constructed event-centric knowledge graphs and the recent typical approaches for event and event relation extraction, besides task description, widely used evaluation datasets, and challenges. Specifically, in the event extraction task, we mainly focus on three recent important research problems: 1) how to learn the textual semantic representations for events in sentence-level event extraction; 2) how to extract relations across sentences or in a document level; 3) how to acquire or augment labeled instances for model training. In event relation extraction, we focus on the extraction approaches for three typical event relation types, including coreference, causal and temporal relations, respectively. Finally, we give out our conclusion and potential research issues in the future.