In the firsc part of the article (chapter 2) a brief review is given of the characteristics of existing and projected accelerators. The second part (chapter 3) is devoted to enumeration of the main problems of elementary-particle physics whose solution depends substantially on the maximum energy achievable in the center-of-mass system: a) the search for an elementary length, i.e., a hypothetical dimensional quantity which provides an energy scale at ultrahigh energies, b) The search for quarks, Schwinger dyons, and other unusual particles, c) The study of self-similar behavior in lepton-hadron and hadron-hadron collisions, particularly the search for deviations from self-similarity which would indicate the appearance of a new energy scale in high-energy physics, d) Further precision experiments in lepton physics in which deviations from the predictions of quantum electrodynamics at ultrasmall distances could be observed, e) The study of weak and weak-electromagnetic processes at high energies. In conclusion a discussion is given of the desirability of constructing a complex of colliding beams of protons, antiprotons, electrons, and positrons with a center-of-mass energy greater than 300 BeV.