In this paper, we investigate the problem of power control for streaming variable bit rate (VBR) videos over wireless links. A system model involving a transmitter (e.g., a base station) that sends VBR video data to a receiver (e.g., a mobile user) equipped with a playout buffer is adopted, as used in dynamic adaptive streaming video applications. In this setting, we analyze power control policies considering the following two objectives: 1) the minimization of the transmit power consumption, and 2) the minimization of the transmission completion time of the communication session. In order to play the video without interruptions, the power control policy should also satisfy the requirement that the VBR video data is delivered to the mobile user without causing playout buffer underflow or overflows. A directional water-filling algorithm, which provides a simple and concise interpretation of the necessary optimality conditions, is identified as the optimal offline policy. Following this, two online policies are proposed for power control based on channel side information (CSI) prediction within a short time window. Dynamic programming is employed to implement the optimal offline and the initial online power control policies that minimize the transmit power consumption in the communication session. Subsequently, reinforcement learning (RL) based approach is employed for the second online power control policy. Via simulation results, we show that the optimal offline power control policy that minimizes the overall power consumption leads to substantial energy savings compared to the strategy of minimizing the time duration of video streaming. We also demonstrate that the RL algorithm performs better than the dynamic programming based online grouped water-filling (GWF) strategy unless the channel is highly correlated.Index Terms-dynamic programming, playout buffer underflow, playout buffer overflow, power control, reinforcement learning, variable bit rate (VBR) video, video streaming.