Abstract: The half-space electromagnetic model is a deterministic model for the various EM problems in air-soil or air-seawater half-space such as remote sensing/imaging/controlling, stealth/anti-stealth design, battlefield reconnaissance and precision guidance of land and sea-based targets. Driven by this engineering applications, in this review, fundamental issues of the half-space integral methods are considered, including the half-space integral equation forms and their corresponding Green's function, the efficient evaluation of Sommerfeld integrals, and the fast solvers. Finally, facing the engineering application requirements, the future works of the half-space integral equation solvers are prospected.