The AMoRE (Advanced Mo-based Rare process Experiment) project is a series of experiments that use advanced cryogenic techniques to search for the neutrinoless double-beta decay of 100 Mo. The work is being carried out by an international collaboration of researchers from eight countries. These searches involve high precision measurements of radiation-induced temperature changes and scintillation light produced in ultra-pure 100 Mo-enriched and 48 Ca-depleted calcium molybdate ( 48depl Ca 100 MoO 4 ) crystals that are located in a deep underground laboratory in Korea. The 100 Mo nuclide was chosen for this 0νββ decay search because of its high Q-value and favorable nuclear matrix element. Tests have demonstrated that CaMoO 4 crystals produce the brightest scintillation light among all of the molybdate crystals, both at room and at cryogenic temperatures. 48depl Ca 100 MoO 4 crystals are being operated at milli-Kelvin temperatures and read out via specially developed metallic-magnetic-calorimeter (MMC) temperature sensors that have excellent energy resolution and relatively fast response times. The excellent energy resolution provides good discrimination of signal from backgrounds, and the fast response time is important for minimizing the irreducible background caused by random coincidence of two-neutrino double-beta decay events of 100 Mo nuclei. Comparisons of the scintillating-light and phonon yields and pulse shape discrimination of the phonon signals will be used to provide redundant rejection of alpha-ray-induced backgrounds. An effective Majorana neutrino mass sensitivity that reaches the expected range of the inverted neutrino mass hierarchy, i.e., 20-50 meV, could be achieved with a 200 kg array of 48depl Ca 100 MoO 4 crystals operating for three years.