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.