Targeted alpha therapy is an oncological treatment, where cytotoxic doses of alpha radiation are locally delivered to tumor cells, while the surrounding healthy tissue is minimally affected. This therapeutic strategy relies on radiopharmaceuticals made of medically relevant radionuclides chelated by ligands, and conjugated to targeting vectors, which promote the drug accumulation in tumor sites. This review discusses the state-of-the-art in the development of radiopharmaceuticals for targeted alpha therapy, breaking down their key structural components, such as radioisotope, targeting vector, and delivery formulation, and analyzing their pros and cons. Moreover, we discuss current drawbacks that are holding back targeted alpha therapy in the clinic, and identify ongoing strategies in field to overcome those issues, including radioisotope encapsulation in nanoformulations to prevent the release of the daughters. Lastly, we critically discuss potential opportunities the field holds, which may contribute to targeted alpha therapy becoming a gold standard treatment in oncology in the future.