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The lack of a shallow donor in diamond with reasonable room temperature conductivity has been a major obstacle, until now, for the realization of many diamond based electronic devices. Most recently it has been shown that exposure of p-type (B doped) homoepitaxial diamond layers to a deuterium plasma can result in the formation of n-type diamond with a shallow donor state (Ea=0.34 eV) and high room temperature mobility (430 cm2/V s) [Z. Teukam et al., Nat. Mater. 2, 482 (2003); C. Saguy et al., Diamond Relat. Mater. 13, 700 (2004)]. Experimental results, based on the comparison of secondary ion mass spectrometry profiles of B and D and Hall effect measurements at different temperatures are presented. They confirm the previous speculation that some deuterium related complex is responsible for the donor activity in diamond. These donors are shown to be formed in a two-step process. First, deuterium diffuses into the entire B containing layer rather slowly, being trapped by the boron acceptors and passivating them. Once all B have formed complexes, further exposure to a D plasma results in the formation of a layer that contains about twice as many D atoms as the B content. This step is the one that gives rise to the excellent n-type features observed. The most recent theoretical attempts to explain the donor state by simulations of various boron-hydrogen complexes in diamond are reviewed. [ABSTRACT FROM AUTHOR]