This review presents an overview of the successes and challenges currently faced in alpha radionuclide therapy. Alpha particles have an advantage in killing tumour cells as compared to beta or gamma radiation due to their short penetration depth and high linear energy transfer (LET). Touching briefly on the clinical successes of radionuclides emitting only one alpha particle, the main focus of this article lies on those alpha-emitting radionuclides with multiple alpha-emitting daughters in their decay chain. While having the advantage of longer half-lives, the recoiled daughters of radionuclides like 224Ra (radium), 223Ra, and 225Ac (actinium) can do significant damage to healthy tissue when not retained at the tumour site. Three different approaches to deal with this problem are discussed: encapsulation in a nano-carrier, fast uptake of the alpha emitting radionuclides in tumour cells, and local administration. Each approach has been shown to have its advantages and disadvantages, but when larger activities need to be used clinically, nano-carriers appear to be the most promising solution for reducing toxic effects, provided there is no accumulation in healthy tissue.