Real-world graphs often contain spatio-temporal information and evolve over time. Compared with static graphs, spatio-temporal graphs have very different characteristics, presenting more significant challenges in data volume, data velocity, and query processing. In this paper, we describe three representative applications to understand the features of spatio-temporal graphs. Based on the commonalities of the applications, we define a formal spatio-temporal graph model, where a graph consists of location vertices, object vertices, and event edges. Then we discuss a set of design goals to meet the requirements of the applications: (i) supporting up to 10 billion object vertices, 10 million location vertices, and 100 trillion edges in the graph, (ii) supporting up to 1 trillion new edges that are streamed in daily, and (iii) minimizing cross-machine communication for query processing. We propose and evaluate PAST, a framework for efficient PArtitioning and query processing of Spatio-Temporal graphs. Experimental results show that PAST successfully achieves the above goals. It improves query performance by orders of magnitude compared with state-of-the-art solutions, including JanusGraph, Greenplum, Spark and ST-Hadoop.