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This paper reviews the main experimental techniques and the most significant results in the searches for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>ϵ</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϵ</mi><msup><mi>β</mi><mo>+</mo></msup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><msup><mi>β</mi><mo>+</mo></msup></mrow></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><msup><mi>β</mi><mo>−</mo></msup></mrow></semantics></math></inline-formula> 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.