We consider the problem of optimal rate allocation and admission control for adaptive video streaming sessions in wireless networks with user dynamics. The central aim is to achieve an optimal tradeoff between several key objectives: maximizing the average rate utility per user, minimizing the temporal rate variability, and maximizing the number of users supported. We identify the structure of algorithms that achieve asymptotically optimal performance in large-capacity systems, and exploit the insight into this structure to devise parsimonious and robust online algorithms. Extensive simulation experiments demonstrate that the proposed online algorithms perform well, even in systems with relatively small capacity.