Amyloidoses is a group of diseases characterized by the accumulation of abnormal proteins (called amyloids) in different organs and tissues. For systemic amyloidoses, the disease is related to increased levels and/or abnormal synthesis of certain proteins in the organism due to pathological processes, e.g., monoclonal gammopathy and chronic inflammation in rheumatic arthritis. Treatment of amyloidoses is focused on reducing amyloidogenic protein production and inhibition of its aggregation. Therapeutic approaches critically depend on the type of amyloidosis, which underlines the importance of early differential diagnostics. In fact, the most accurate diagnostics of amyloidosis and its type requires analysis of a biopsy specimen from the disease-affected organ. However, absence of specific symptoms of amyloidosis and the invasive nature of biomaterial sampling causes the late diagnostics of these diseases, which leads to a delayed treatment, and significantly reduces its efficacy and patient survival. The establishment of noninvasive diagnostic methods and discovery of specific amyloidosis markers are essential for disease detection and identification of its type at earlier stages, which enables timely and targeted treatment. This review focuses on current approaches to the diagnostics of amyloidoses, primarily with renal involvement, and research perspectives in order to design new specific tests for early diagnosis.