Over the past few decades, significant attention has been paid to the biomedical applications of terahertz (THz) technology. Nowadays, THz spectroscopy and imaging have allowed numerous demanding problems in the biological, medical, food, plant and pharmaceutical sciences to be solved. Among the biomedical applications, the label-free diagnosis of malignant and benign neoplasms represents one of the most attractive branches of THz technology. Despite this attractiveness, THz diagnosis methods are still far from being ready for use in medical practice. In this review, we consider modern research results in the THz diagnosis of malignant and benign neoplasms, along with the topical research and engineering problems which restrain the translation of THz technology to clinics. We start by analyzing the common models of THz-wave-tissue interactions and the effects of tissue exposure to THz waves. Then, we discuss the existing modalities of THz spectroscopic and imaging systems, which have either already been applied in medical imaging, or hold strong potential. We summarize the earlier-reported and original results of the THz measurements of neoplasms with different nosology and localization. We pay attention to the origin of contrast between healthy and pathological tissues in the THz spectra and images, and discuss the prospects of THz technology in