Cancer is one of the major causes of death worldwide and its treatment remains very challenging. The effectiveness of cancer therapy significantly depends upon tumour-specific delivery of the drug. Nanoparticle drug delivery systems have been developed to avoid the side effects of the conventional chemotherapy. However, according to the most recent recommendations, future nanomedicine should be focused mainly on active targeting of nanocarriers based on ligand-receptor recognition, which may show better efficacy than passive targeting in human cancer therapy. Nevertheless, the efficacy of single-ligand nanomedicines is still limited due to the complexity of the tumour microenvironment. Thus, the NPs are improved toward an additional functionality, e.g., pH-sensitivity (advanced single-targeted NPs). Moreover, dual-targeted nanoparticles which contain two different types of targeting agents on the same drug delivery system are developed. The advanced single-targeted NPs and dual-targeted nanocarriers present superior properties related to cell selectivity, cellular uptake and cytotoxicity toward cancer cells than conventional drug, non-targeted systems and single-targeted systems without additional functionality. Folic acid and biotin are used as targeting ligands for cancer chemotherapy, since they are available, inexpensive, nontoxic, nonimmunogenic and easy to modify. These ligands are used in both, single- and dual-targeted systems although the latter are still a novel approach. This review presents the recent achievements in the development of single- or dual-targeted nanoparticles for anticancer drug delivery.