We address the problem of agile and rapid locomotion, a key characteristic of quadrupedal and bipedal robots. We present a new algorithm that maintains stability and generates high-speed trajectories by considering the temporal aspect of locomotion. Our formulation takes into account past information based on a novel history-aware curriculum Learning (HACL) algorithm. We model the history of joint velocity commands with respect to the observed linear and angular rewards using a recurrent neural net (RNN). The hidden state helps the curriculum learn the relationship between the forward linear velocity and angular velocity commands and the rewards over a given time-step. We validate our approach on the MIT Mini Cheetah,Unitree Go1, and Go2 robots in a simulated environment and on a Unitree Go1 robot in real-world scenarios. In practice, HACL achieves peak forward velocity of 6.7 m/s for a given command velocity of 7m/s and outperforms prior locomotion algorithms by nearly 20%.