Machine translation of natural language (MT) was one of the main subjects of study for those who were interested in the applications of the electronic computer just after it was put to practical use. Various kinds of researches and experiments had been performed up until 1966,when the ALPAC report was published in the U.S.A.. Then the main interests of the related researchers shifted from MT to subjects such as machine understanding of natural language, question-answering systems, or more basic researches of natural language. But recently, interest in MT seems to have returned. The author believes at this juncture that a thorough examination and reconsideration of the results and the controversial points of the past researches should be performed at the outset, and that new guiding principles in MT research should be established. This paper, therefore, outlines the underlying theories and methodology of MT used by various researchers (including myself) in the past. The intrinsic problems of translation of natural language, the differences of conditions and environments between translation perfommed by human beings and those performed by machines are also discussed. Finally we briefly discuss goals for the future of MT, and problems to be solved in order to approach those goals.