Amino acid transporters are abundant amongst the solute carrier family and have an important role in facilitating the transfer of amino acids across cell membranes. Because of their impact on cell nutrient distribution, they also appear to have an important role in the growth and development of cancer. Naturally, this has made amino acid transporters a novel target of interest for the development of new anticancer drugs. Many attempts have been made to develop inhibitors of amino acid transporters to slow down cancer cell growth, and some have even reached clinical trials. The purpose of this review is to help organize the available information on the efforts to discover amino acid transporter inhibitors by focusing on the amino acid transporters ASCT2 (SLC1A5), LAT1 (SLC7A5), xCT (SLC7A11), SNAT1 (SLC38A1), SNAT2 (SLC38A2), and PAT1 (SLC36A1). We discuss the function of the transporters, their implication in cancer, their known inhibitors, issues regarding selective inhibitors, and the efforts and strategies of discovering inhibitors. The goal is to encourage researchers to continue the search and development within the field of cancer treatment research targeting amino acid transporters.