The formation of Λ hypernuclear systems through kaon photo and electroproduction is theoretically investigated. Utilizing the single virtual photon exchange approximation and density matrix formalism, general relations between the production cross section and hadronic current are developed. The current is expressed in terms of elementary virtual photoproduction ( γ Vp→K + Λ) amplitudes that are explicitly evaluated from diagrams representing the exchange of s and u channel baryons (p, Λ, Σ 0) and t channel mesons (K, K ∗). Using coupling constants from a phenomenological photoproduction analysis and kaon form factors governed by the φ meson (vector dominance model), a reasonable description of the limited p(e, e K)Λ data is obtained. Relativistic, covariant calculations for deuteron electrodisintegration, d(e, e K)Λn, are also reported which document the cross section sensitivity to the kaon form factor and dnp vertex function (deuteron wavefunction). The sensitivity to the Λn final state interaction is also examined and the utility of this reaction for investigating controversial strange dibaryon resonances is discussed. The excitation spectrum for hypernuclear formation from 4He and 12C targets is calculated and optimum kinematics for extracting the longitudinal hypernuclear structure function are determined. Finally, count rates supporting the feasibility of selected experiments are provided for existing low duty cycle and proposed high duty cycle facilities.