We review the results of recent studies and calculations of Λ-hypernuclear excitations via electromagnetic probes [the (e, e′K+) and (γ, K+) reactions]. After discussing the importance of the probe, we present and analyze the theoretical features of a model (based on Feynman diagrams) for studying the process. The special kinematics of the nuclear (e, e′K+) reaction, involving high momentum transfers, is discussed. We then present cross section calculations. Using first a nonrelativistic nuclear structure model, we present results for the exclusive and inclusive electromagnetic hypernuclear excitations and for a large range of nuclear masses. Next, we calculate cross sections using the fully-relativistic form of the transition operator and relativistic Dirac-nuclear-and hypernuclear- structure model. In this context, we analyze the effects of the large scalar and vector potentials of the relativistic model and of the Dirac-spinor wave functions of the proton and the Λ-hyperon, on the calculated quantity. The relativistic-model calculations are presented for both pseudoscalar (PS) and pseudovector (PV) KNΛ vertex couplings and we discuss in detail the different theoretical predictions obtained in the two cases. Throughout the paper, we emphasize several uncertainties regarding the determination of coupling constants, PS vs PV coupling schemes, and relativistic uncertainties. Finally, we present technical and experimental considerations for the study of the (e, e′K+) and (γ, K+) reactions at the continuous electron beam accelerator facility (CEBAF), which is currently under construction in Newport News, Virginia.