Eddy current (EC) testing has become one of the most common techniques for measuring metallic planar structures in various industrial scenarios such as infrastructures, automotive, manufacturing, and chemical engineering. There has been significant progress in measuring the geometry, electromagnetic properties, and defects of metallic planar structures based on electromagnetic principles. In this review, we summarize recent developments in EC computational models, systems, algorithms, and measurement approaches for planar structures. First, the computational models including analytical models, numerical methods, and plate property estimation algorithms are introduced. Subsequently, the impedance measurement system and probes are presented. In plate measurements, sensor signals are sensitive to probe lift-off, and various algorithms for reducing the lift-off effect are reviewed. These approaches can be used for measureing thickness and electromagnetic properties. Furthermore, defect detection for metallic plates is also discussed.