Classical reaction kinetics has been found to be unsatisfactory when the reactants are spatially constrained on the microscopic level by either walls, phase boundaries, or force fields. Recently discovered theories of heterogeneous reaction kinetics have dramatic consequences, such as fractal orders for elementary reactions, self-ordering and self-unmixing of reactants, and rate coefficients with temporal ``memories.'' The new theories were needed to explain the results of experiments and supercomputer simulations of reactions that were confined to low dimensions or fractal dimensions or both. Among the practical examples of ``fractal-like kinetics'' are chemical reactions in pores of membranes, excitation trapping in molecular aggregates, exciton fusion in composite materials, and charge recombination in colloids and clouds. Diffusion-controlled reactions with geometrical constraints, as found in heterogeneous kinetics, may be described by reactions on fractal domains. The hallmarks of ``fractal-like'' reactions are anomalous reaction orders and time-dependent reaction rate ``constants.'' These anomalies stem from the nonrandomness of the reactant distributions in low dimensions. For homo-bimolecular reactions (A + A --> Pr) the distribution is partially ordered, for example, quasi-periodic. However, for hetero-bimolecular reactions (A + B --> Pr) the reactants segregate. Theory, simulations, and experiments are interrelated through the formalism of fractal reaction kinetics (42).