Drostie's post provides an excellent summary of the process of measuring this, though there are more experiments than GERDA in the works - two that come to mind

Drostie's post provides an excellent summary of the process of measuring this, though there are more experiments than GERDA in the works - two that come to mind immediately are SuperNEMO (https://en.wikipedia.org/wiki/Neutrino_Ettore_Majorana_Observatory https://en.wikipedia.org/wiki/Neutrino_Ettore_Majorana_Obser...) and SNO+ (https://en.wikipedia.org/wiki/SNO%2B https://en.wikipedia.org/wiki/SNO%2B) - Additionally I'd be remiss in not mentioning COBRA (http://www.cobra-experiment.org/ http://www.cobra-experiment.org/) which was around a few years ago but I'm not sure of the current status. As far as the "Popularity" - I'm sure there are groups of theoretical physicists that work purely on the assumption of one or the other, but most treatments I've seen cover both the cases for Dirac and Majorana neutrinos, given that we don't have evidence one way or the other.