This paper reviews the main experimental techniques and the most significant results in the searches for the 2ϵ, ϵβ+ and 2β+ decay modes. Efforts related to the study of these decay modes are important, since they can potentially offer complementary information with respect to the cases of 2β− decays, which allow a better constraint of models for the nuclear structure calculations. Some positive results that have been claimed will be mentioned, and some new perspectives will be addressed shortly.