In the past ten years, neutrino oscillation experiments have provided the incontrovertible evidence that neutrinos mix and have finite masses. These results represent the strongest demonstration that the electroweak Standard Model is incomplete and that new Physics beyond it must exist. In this scenario, a unique role is played by the Neutrinoless Double Beta Decay searches which can probe lepton number conservation and investigate the Dirac/Majorana nature of the neutrinos and their absolute mass scale (hierarchy problem) with unprecedented sensitivity. Today Neutrinoless Double Beta Decay faces a new era where large-scale experiments with a sensitivity approaching the so-called degenerate-hierarchy region are nearly ready to start and where the challenge for the next future is the construction of detectors characterized by a tonne-scale size and an incredibly low background. A number of new proposed projects took up this challenge. These are based either on large expansions of the present experiments or on new ideas to improve the technical performance and/or reduce the background contributions. In this paper, a review of the most relevant ongoing experiments is given. The most relevant parameters contributing to the experimental sensitivity are discussed and a critical comparison of the future projects is proposed.