Monoclonal gammopathy of undetermined significance (MGUS) is characterized by a serum monoclonal protein <30 g/l, <10% plasma cells in the bone marrow, and absence of end‐organ damage (CRAB–hypercalcaemia, renal insufficiency, anaemia, or bone lesions). MGUS is present in 3% of persons >50 years and in 5% >70 years of age. The risk of progression to multiple myeloma (MM) or a related disorder is 1% per year. Patients with risk factors consisting of an abnormal serum free light chain ratio, non‐immunoglobulin G (IgG) MGUS, and an elevated serum M protein ≥15 g/l had a risk of progression at 20 years of 58%, compared with 37% with two risk factors present, 21% with one risk factor present, and 5% when none of the risk factors were present. Smouldering (asymptomatic) multiple myeloma is characterized by having a serum IgG or IgA monoclonal protein of 30 g/l or higher and/or 10% or more plasma cells in the bone marrow but no evidence of end‐organ damage. The cumulative probability of progression to active MM or amyloidosis was 51% at 5 years, 66% at 10 years and 73% at 15 years; the median time to progression was 4·8 years.