Fine needle aspiration cytology (FNAC) and core needle biopsy (CNB) are widely used in diagnosing breast lesions, with both achieving high sensitivity and specificity. Whether FNAC or CNB is better remains highly controversial. In this review, the advantages and disadvantages of each of these methods are discussed, especially in relation to specific problematic groups of breast lesions. In general, CNB has a slight advantage with lower inadequate and suspicious rates, allowing easier grade assessment and ancillary testings (hormome receptors, HER2) in cases of cancers. FNAC cannot reliably predict invasion in a malignant aspirate, whereas CNB, although useful in confirming invasion in carcinomas, has a much lower efficacy in predicting invasion when only in situ carcinoma is detected. The other problematic areas are papillary breast lesions and fibroepithelial lesions, notably phyllodes tumors. In papillary lesions, FNAC diagnosis is inaccurate, but with CNB, one can confidently diagnose papillary lesion, although there is still significant false positive and false negative rates, even with immunohistochemistry. For fibroepithelial lesions, using either FNAC or CNB to differentiate between a phyllodes tumor from fibroadenoma is also inaccurate. As management of breast diseases necessitates the triple approach (clinical, imaging and pathological), an awareness of the limitations of these very useful diagnostic modalities by all specialists is prudent, especially when dealing with these specific groups of breast lesions.