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Kinematic variables have been playing an important role in collider phenomenology, as they expedite discoveries of new particles by separating signal events from unwanted background events and allow for measurements of particle properties such as masses, couplings, spins, etc. For the past 10 years, an enormous number of kinematic variables have been designed and proposed, primarily for the experiments at the Large Hadron Collider, allowing for a drastic reduction of high-dimensional experimental data to lower-dimensional observables, from which one can readily extract underlying features of phase space and develop better-optimized data-analysis strategies. We review these recent developments in the area of phase space kinematics, summarizing the new kinematic variables with important phenomenological implications and physics applications. We also review recently proposed analysis methods and techniques specifically designed to leverage the new kinematic variables. As machine learning is nowadays percolating through many fields of particle physics including collider phenomenology, we discuss the interconnection and mutual complementarity of kinematic variables and machine learning techniques. We finally discuss how the utilization of kinematic variables originally developed for colliders can be extended to other high-energy physics experiments including neutrino experiments.