Deep-earth engineering is a strategic national priority, and the structural integrity of drilling equipment is essential for safe operation. As a key enabling technology, electromagnetic nondestructive testing has attracted significant attention owing to its high efficiency, high sensitivity, and capability for quantitative defect characterization. However, the large-scale and complex structures of deep-earth drilling equipment, together with harsh operating conditions, impose stringent requirements on detection accuracy, environmental adaptability, and intelligence inspection. This article reviews the research progress and development trends of electromagnetic testing technologies. Based on the fundamental mechanisms of electromagnetic induction, electromagnetic diffusion, and multiphysics coupling, the principles, applications, advantages, and limitations of eddy current testing, pulsed eddy current testing, magnetic eddy current testing, magnetic flux leakage testing, alternating current field measurement, and electromagnetic acoustic testing are summarized. The key challenges associated with reliability and automation under high-temperature, high-pressure, thick-walled, multilayer, and high-noise conditions are further discussed. Finally, future research directions are highlighted from the perspectives of advanced sensing, novel excitation methods, and intelligent inversion, and a closed-loop inspection framework integrating perception, decision-making, execution, and optimization is proposed. This review provides a systematic reference for the application and development of electromagnetic testing technologies in deep-earth drilling engineering.