The recent progress in theoretical description of the neutrinoless double beta decay ($0\nu\beta\beta$-decay) is briefly reviewed. By taking advantage of an interpolating formula, which allows to calculate the $0\nu\beta\beta$-decay half-life for an arbitrary neutrino mass and which is expressed with a single nuclear matrix element, neutrino mass mechanisms of this process having origin in the left-right symmetric models are discussed. To understand the importance of the mass mechanism due to right-handed leptonic current, an assumption about seesaw-type $6\times 6$ unitary neutrino mixing matrix and relation of light and heavy neutrino masses is made. The region of dominance of right over left leptonic current mechanisms is identified. Further, a progress in the calculation of double beta decay nuclear matrix elements within the quasiparticle random phase approximation is reported. A connection between the two neutrino double-beta decay and $0\nu\beta\beta$-decay matrix elements is discussed. An impact of the quenching of the axial-vector coupling constant $g_A$ on double-beta decay processes is addressed and a possibility to determine quenched value of $g_A$ is announced.