Hyaluronic acid (HA) has been implemented for chemo and photothermal therapy to target tumour cells overexpressing the CD44+ receptor. HA-targeting hybrid systems allows carbon nanomaterial (CNM) carriers to efficiently deliver anticancer drugs, such as doxorubicin and gemcitabine, to the tumour sites. Carbon nanotubes (CNTs), graphene, graphene oxide (GO), and graphene quantum dots (GQDs) are grouped for a detailed review of the novel nanocomposites for cancer therapy. Some CNMs proved to be more successful than others in terms of stability and effectiveness at removing relative tumour volume. While the literature has been focused primarily on the CNTs and GO, other CNMs such as carbon nano-onions (CNOs) proved quite promising for targeted drug delivery using HA. Near-infrared laser photoablation is also reviewed as a primary method of cancer therapy—it can be used alone or in conjunction with chemotherapy to achieve promising chemo-photothermal therapy protocols. This review aims to give a background into HA and why it is a successful cancer-targeting component of current CNM-based drug delivery systems.