Summary form only given. Fundamental problems of plasma fusion (controlled thermonuclear fusion) due to the contradicting demands of the magnetic confinement of plasma and suppression of instabilities occurring on and in plasma are surveyed in contrast with problems of cold fusion. Problems in cold fusion due to the complicated constituents and types of force are explained. Typical cold fusion events are explained by a model based on the presence of trapped neutrons in cold fusion materials. The events include Pons-Fleishmann effect, tritium anomaly, helium 4 production, and nuclear transmutation. The fundamental hypothesis of the model is an effectiveness of a new concept-neutron affinity of elements. The neutron affinity is defined and some bases supporting it are explained. Possible justification of the concept by a statistical approach is given.