Abstract: Microwave irradiation becomes a widely used method to synthesize many useful organic chemicals rapidly, with good yields and high selectivity. A great many of relevant works suggest only thermal nature of the microwave action, that means that microwaves are considered to be a method to heat chemical reagents rapidly and without any overheating. Some other works describe specific non-thermal effects. And the effects are likely to exist. Sometimes the effects are thought to be only specific forms of heat effects, but not always. We have recently observed some of the effects in the microwave initiated polymerizations and oxidations when the microwave power was quite low [1-3]. Here we shall try to discuss briefly possibilities that can be useful to explain the microwave effects. The discussion suggests selection of theoretical ideas that will serve a basis for future theories of the microwave-initiated reactions.