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Twenty years ago in the first issue of IJHR, among others, there was a published paper [M. Vukobratović and B. Borovac, Zero-moment point - Thirty five years of its life, Int. J. Humanoid Robot. 1(1) (2004) 157–173], devoted to well-known zero-moment point (ZMP) concept. Its role in biped locomotion (in the preservation of dynamic balance during walking and gait synthesis) was (and still is) extremely significant. This paper is aimed to present, how far we have gone in the past 20 years in the realization of bipedal walking, what are remaining open challenges and what we can expect in the further development. At the beginning of the paper, we will briefly refer to some still existing misinterpretations of the ZMP notion, related to specific boundary cases, when the terms Center of Pressure (CoP) and ZMP are still being mixed. Then, we will point your attention to the discussion of two important issues: attempts of generalization of ZMP notion in case of motion in the presence of multiple, spatially distributed and non-planar contacts and walk realization in a non-laboratory environment (unstructured environment and on the non-flat ground surface). Of course, looking at \how humans do it" has always been an inspiration for the realization of complex tasks by humanoids. Learning to walk is a task where several successful realizations have appeared only recently, so we will look at this topic at the end of this paper. © World Scientific Publishing Company.