This paper provides a systematic review and analysis of different phenomena that violate a basic principle, Kasha's rule, when applied to photochemical reactions. In contrast to the classical route of ultrafast transition to the lowest energy excited state and photochemical reaction starting therein, in some cases, these reactions proceed directly from high-energy excited states. Nowadays, this phenomenon can be observed for a number of major types of excited-state reactions: harvesting product via intersystem crossing; photoisomerizations; bond-breaking; and electron, proton, and energy transfers. We show that specific conditions for their observation are determined by kinetic factors. They should be among the fastest reactions in studied systems, competing with vibrational relaxation and radiative or nonradiative processes occurring in upper excited states. The anti-Kasha effects, which provide an important element that sheds light on the mechanisms of excited-state transformations, open new possibilities of selective control of these reactions for a variety of practical applications. Efficient utilization of excess electronic energy should enhance performance in the systems of artificial photosynthesis and photovoltaic devices. The modulation of the reporting signal by the energy of excitation of light should lead to new technologies in optical sensing and imaging.