Plug-in hybrid electric vehicles (PHEVs) have emerged as an important tool in reducing greenhouse gas emissions, due to their lower dependency on fossil fuel. Since, for cost efficiency, PHEVs have a limited battery capacity, they must be recharged often and especially after trips. Thus, efficient battery charging plays an important role on the success of PHEVs commercial adoption. This paper surveys the state-of-the-art of existing PHEV battery charging schemes. We classify these schemes into four classes, namely, uncontrolled , indirectly controlled , smart , and bidirectional charging, and review various existing techniques within each class. For uncontrolled charging, existing studies focus on evaluating the impact of adding variable charging load on the smart grid. Various indirectly controlled charging schemes have been proposed to control energy prices, in order to indirectly influence the charging operations. Smart charging schemes can directly control a rich set of charging parameters to achieve various performance objectives, such as minimizing power loss, maximizing operator’s profit, ensuring fairness, and so on. Finally, bidirectional charging allows a PHEV to discharge energy into smart grid, such that the vehicle can act as a mobile energy source to further stabilize the grid, which is partially supplied by intermittent renewable energy sources. This survey provides a comprehensive one-stop introductory reference to quickly learn about the key features and technical challenges, addressed by existing PHEV battery charging schemes in smart grid.