Diabetic nephropathy is one of the most frequent complications in type 1 and type 2 diabetes and the leading cause of chronic kidney disease (CKD) in patients starting renal replacement therapy in developed countries. Early detection along with multifactorial treatments, such as blood glucose control with sodium glucose cotransporter 2 inhibitors and blood pressure control with renin-angiotensin system blockers, are of particular importance to prevent disease progression and reduce mortality. In clinical settings, diabetic nephropathy is typically diagnosed by detecting microalbuminuria, the earliest indicator of this disease, in patients with diabetes for whom other causes of albuminuria are absent. However, recent renal biopsy based studies have demonstrated that albuminuria is neither a specific nor a sensitive biomarker for the development of diabetic nephropathy. The classical diabetic nephropathy is characterized by the progressive increase of albuminuria from normoalbuminuria to microalbuminuria and macroalbuminuria, declining glomerular filtration rate (GFR), and eventual end-stage renal disease. However, the clinical course of diabetic nephropathy has changed profoundly in recent years, due to the diversification of diabetes, therapeutic successes, as well as an aging population. Indeed, CKD attributable to diabetes which runs an atypical clinical course (i.e., so-called non-albuminuric renal function decline) has increased over the past decades. The paradigm shift from albuminuria-based to GFR-based kidney disease results in a new concept of diabetic kidney disease (DKD). This review article describes the concept of DKD, and differences between classical diabetic nephropathy and DKD.