Breast cancer (BC) is the most frequent malignant cancer diagnosis and is a primary factor for cancer deaths in women. The clinical subtypes of BC include estrogen receptor (ER) positive, progesterone receptor (PR) positive, human epidermal growth factor receptor 2 (HER2) positive, and triple-negative BC (TNBC). Based on the stages and subtypes of BC, various treatment methods are available with variations in the rates of progression-free disease and overall survival of patients. However, the treatment of BC still faces challenges, particularly in terms of drug resistance and recurrence. The study of epigenetics has provided new ideas for treating BC. Targeting aberrant epigenetic factors with inhibitors represents a promising anticancer strategy. The KDM5 family includes four members, KDM5A, KDM5B, KDM5C, and KDMD, all of which are Jumonji C domain-containing histone H3K4me2/3 demethylases. KDM5 proteins have been extensively studied in BC, where they are involved in suppressing or promoting BC depending on their specific upstream and downstream pathways. Several KDM5 inhibitors have shown potent BC inhibitory activity in vitro and in vivo, but challenges still exist in developing KDM5 inhibitors. In this review, we introduce the subtypes of BC and their current therapeutic options, summarize KDM5 family context-specific functions in the pathobiology of BC, and discuss the outlook and pitfalls of KDM5 inhibitors in this disease.