Currently, there is an intensive development of bipedal walking robots. The most known solutions are based on the use of the principles of human gait created in nature during evolution. Modernbipedal robots are also based on the locomotion manners of birds. This review presents the current state of the art of bipedal walking robots based on natural bipedal movements (human and bird) as well as on innovative synthetic solutions. Firstly, an overview of the scientific analysis of human gait is provided as a basis for the design of bipedal robots. The full human gait cycle that consists of two main phases is analysed and the attention is paid to the problem of balance and stability, especially in the single support phase when the bipedal movement is unstable. The influences of passive or active gait on energy demand are also discussed. Most studies are explored based on the zero moment. Furthermore, a review of the knowledge on the specific locomotor characteristics of birds, whose kinematics are derived from dinosaurs and provide them with both walking and running abilities, is presented. Secondly, many types of bipedal robot solutions are reviewed, which include nature-inspired robots (human-like and birdlike robots) and innovative robots using new heuristic, synthetic ideas for locomotion. Totally 45 robotic solutions are gathered by thebibliographic search method. Atlas was mentioned as one of the most perfect human-like robots, while the birdlike robot cases were Cassie and Digit. Innovative robots are presented, such asslider robot without knees, robots with rotating feet (3 and 4 degrees of freedom), and the hybrid robot Leo, which can walk on surfaces and fly. In particular, the paper describes in detail the robots’ propulsion systems (electric, hydraulic), the structure of the lower limb (serial, parallel, mixed mechanisms), the types and structures of control and sensor systems, and the energy efficiency of the robots. Terrain roughness recognition systems using different sensor systems based on light detection and ranging or multiple cameras are introduced. A comparison of performance, control and sensor systems, drive systems, and achievements of known human-like and birdlike robots is provided. Thirdly, for the first time, the review comments on the future of bipedal robots in relation to the concepts of conventional (natural bipedal) and synthetic unconventional gait. We critically assess and compare prospective directions for further research that involve the development of navigation systems, artificial intelligence, collaboration with humans, areas for the development of bipedal robot applications in everyday life, therapy, and industry.