We have proposed methods for generating energy-efficient dynamic bipedal gait based on passive dynamics. Parametrically excited dynamic bipedal walking is a novel approach to efficient level dynamic walking. In this method, the robot restores mechanical energy by pumping the telescopic legs without using any rotary actuators, and stable ZMP-free walking on level ground is then easily achieved. This method has also been extended to the cases of knee-joint actuation and ornithoid walking. In this presentation, we first outline the mathematical modeling, control laws, numerical simulations, and experimental results. Second, we introduce our method for generating an asymptotic stable gait based on the stability principle of a rimless wheel, and explain the importance of controlling mechanical energy in enhancing the asymptotic stability. We also analyzed the efficiency of asymmetric 2-period gait using an asymmetric rimless wheel model. Through the theoretical analysis, we found there is a possibility that asymmetric 2-period gait is less efficient than symmetric 1-period one in terms of the walking speed. We finally talk about our recent results on the effect of delayed feedback control (DFC) on the gait efficiency. We apply DFC to a parametrically excited walker with knees and examine how the walking speed and the stable domain change after the stabilization to 1-period gait. Based on the numerical results, we discuss about the role of period-doubling bifurcation in limit cycle walking.