Nuclear fusion between deuterons under ambient conditions has been observed in the metal cathode of an electrolysis cell with an electrolyte of heavy water. The evidence for the fusion reaction is derived primarily from the detection of a low level of 2.45-MeV neutrons presumably from the neutron branch of the deuterium fusion reaction. However, the estimated fusion energy yield associated with the neutron output is insufficient to account for the majority of the reported energy gain if the neutron-proton branch of the deuterium fusion reaction remains about equal to ambient conditions. The excess energy gain may arise from an unobserved chemical reaction or an unfamiliar nuclear reaction. Reported evidence of an excess of 4He in the vicinity of the cathode may indicate that a 4He branch from the deuterium fusion reaction may proceed at ambient conditions through internal electron conversion without a large release of gamma rays. These issues are explored, and attempts are made to provide physical mechanisms and explanations for the cold fusion experimental observations.