The renal deposition of monoclonal immunoglobulins can cause severe renal complications in patients with B cell and plasma cell lymphoproliferative disorders. The overproduction of a structurally unique immunoglobulin can contribute to the abnormal propensity of monoclonal immunoglobulins to aggregate and deposit in specific organs. A wide range of renal diseases can occur in multiple myeloma or monoclonal gammopathy of renal significance, including tubular and glomerular disorders with organized or unorganized immunoglobulin deposits. The development of reliable experimental models is challenging owing to the inherent variability of immunoglobulins and the heterogeneity of the pathologies they produce. However, although imperfect, animal models are invaluable tools to understand the molecular pathogenesis of these diseases, and advances in creating genetically modified animals might provide novel approaches to evaluate innovative therapeutic interventions. We discuss the strategies employed to reproduce human monoclonal immunoglobulin-induced kidney lesions in animal models, and we highlight their advantages and shortcomings. We also discuss how these models have affected the management of these deposition diseases and might do so in the future. Finally, we discuss hypotheses that explain some limitations of the various models, and how these models might improve our understanding of other nephropathies without immunoglobulin involvement that have similar pathogenic mechanisms.