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Propagation and reflection of electromagnetic waves in time-varying dielectric media are studied using analytic solutions of the relevant Maxwell equations. Exactly solvable models that do not involve any requirements of small or slow changes in the medium reveal strong nonstationarity-induced dispersion effects due to a finite relaxation time of the dielectric parameters. The generalized time-dependent Fresnel and Snell laws visualizing the dependence of reflection coefficients on the dynamics of reflecting media are presented. The drastic distortion of EM fields interacting with rapidly ionizing plasmas is examined. The coupled spatiotemporal reshaping of wave fields in heterogeneous time-varying media is considered for transmission lines, heterogeneous dielectrics, and flash ionization in microwave cavities. The efficiency of the time-domain approach in treating these problems is demonstrated.