Breast cancer stem(-like) cells (BCSCs) have been found to be responsible for therapeutic resistance and disease relapse. BCSCs are difficult to eradicate due to their high resistance to conventional treatments and high plasticity. Functionalised nanoparticles have been investigated as smart vehicles to transport across various barriers and increase the interaction of therapeutic agents with cancer cells, as well as BCSCs. In this review, we discuss the different characteristics of BCSCs, and challenges to tackle BCSCs at cellular and molecular levels. The mechanisms of action and physicochemical properties of the current BCSC targeting agents are also covered. We will focus on the rational design and recent advances of "Nano + Nano" or single tumour targeting nanoparticle systems loaded with dual or multiple agents to kill all cancer cells including BCSCs. These cocktail therapies include the combination of a chemotherapy agent with a BCSC-specific inhibitor, a phytochemical agent or RNA based therapy. Given the heterogeneity of breast tumour tissue, targeting both BCSCs and bulk breast cancer cells simultaneously with multiple agents holds great promise in eliminating breast cancer. The future research needs to focus on overcoming various barriers in the 'clinical translation' of BCSC-targeting nanomedicines to cure breast cancer, which requires a significant multidisciplinary effort.