The 2019 5th edition of the WHO classification of digestive system tumors estimates that up to 35% of hepatocellular carcinomas (HCCs) can be classified as one of eight subtypes defined by molecular characteristics: steatohepatitic, clear cell, macrotrabecular-massive, scirrhous, chromophobe, fibrolamellar, neutrophil-rich, and lymphocyte-rich HCCs. Due to their distinct cellular and architectural characteristics, these subtypes may not display arterial phase hyperenhancement and washout appearance, which are the classic MRI features of HCC, creating challenges in noninvasively diagnosing such lesions as HCC. Moreover, certain subtypes with atypical imaging features have a worse prognosis than other HCCs. A range of distinguishing imaging features may help raise suspicion that a liver lesion represents one of these HCC subtypes. In this review, we describe the MRI features that have been reported in association with various HCC subtypes according to the 2019 WHO classification, with attention given to the current understanding of these subtypes' pathologic and molecular bases and relevance to clinical practice. Imaging findings that differentiate the subtypes from benign liver lesions and non-HCC malignancies are highlighted. Familiarity with these sub-types and their imaging features may allow the radiologist to suggest their presence, though histologic analysis remains needed to establish the diagnosis.