The standard treatment for breast cancer patients at low risk of recurrence is based on conservative surgery followed by radiation therapy delivered to the whole breast. The accelerated partial breast irradiation (APBI) concept, developed more than 15 years ago, could be an option in selected patients. However, the ideal patient profile for APBI is still not clearly identified. Recent reports from the American Society for Radiation Oncology (ASTRO) and the Groupe Européen de Curiethérapie-European Society for Therapeutic Radiology and Oncology (GEC-ESTRO) have suggested selection criteria for "suitable patients" who could receive APBI outside of clinical trials. Currently, there are 6 ongoing phase III trials. All are characterized by a significant heterogeneity regarding inclusion criteria and stratification factors. The French UNICANCER trial (SHARE; ClinicalTrials.gov identifier NCT01247233) will randomize 2,800 patients in 3 arms: APBI (1 week) using 3-dimensional (3D) conformal radiotherapy, standard radiotherapy (6.5 weeks), and hypofractionated radiotherapy (3 weeks). In this article, we review the reported retrospective studies as well as older randomized trials. We will also describe the differences between the 6 ongoing phase III trials and the particularities of the French SHARE trial.