Polyomavirus nephropathy, also termed BK-virus nephropathy (BKN) after the main causative agent, the polyoma-BK-virus strain, is a significant complication after kidney transplantation. BKN is the most common viral infection that affects renal allografts with a prevalence of 1-9% on average 8-13 months post surgery. It can also occur sporadically in native kidneys. Viral nephropathy is caused by the (re)activation of latent BK viruses that enter into a replicative cycle under sustained and intensive immunosuppression. Pure productive kidney infections with JC- and SV-40 polyomaviruses are exceptionally rare. BKN is morphologically defined by the presence of intranuclear viral inclusion bodies in epithelial cells and tubular injury, which is the morphological correlate for renal dysfunction. Renal disease can progress through different histologic stages (from early BKN stage A to late fibrotic stage C) that carry prognostic significance; disease stages B and C often result in chronic kidney (allograft) dysfunction and end-stage renal disease. The clinical goal is to diagnose viral nephropathy in disease stage A and to limit chronic renal injury. Strategies to recognize, classify, and manage BKN are critically discussed including ancillary techniques for risk assessment and patient monitoring: (i) urine cytology and the search for so-called 'decoy cells'; (ii) PCR analyses for viral load measurements in the plasma and urine; and (iii) negative staining urine electron microscopy to identify viral particles.