Abstract-Smart interactions among the smart grid, aggregators and EVs can bring various benefits to all parties involved, e.g., improved reliability and safety for the smart gird, increased profits for the aggregators, as well as enhanced self benefit for EV customers. This survey focus on viewing this smart interactions from an algorithmic perspective. In particular, important dominating factors for coordinated charging from three different perspectives are studied, in terms of smart grid oriented, aggregator oriented and customer oriented smart charging. Firstly, for smart grid oriented EV charging, we summarize various formulations proposed for load flattening, frequency regulation and voltage regulation, then explore the nature and substantial similarity among them. Secondly, for aggregator oriented EV charging, we categorize the algorithmic approaches proposed by research works sharing this perspective as direct and indirect coordinated control, and investigate these approaches in detail. Thirdly, for customer oriented EV charging, based on a commonly shared objective of reducing charging cost, we generalize different formulations proposed by studied research works. Moreover, various uncertainty issues, e.g., EV fleet uncertainty, electricity price uncertainty, regulation demand uncertainty, etc., have been discussed according to the three perspectives classified. At last, we discuss challenging issues that are commonly confronted during modeling the smart interactions, and outline some future research topics in this exciting area.