After a brief survey of Godel's personal contacts with Brouwer and Heyting, examples are discussed where intuitionistic ideas had a direct influence on Godel's technical work. Then it is argued that the closest rapprochement of Godel to intuitionism is seen in the development of the Dialectica Interpretation, during which he came to accept the notion of computable functional of finite type as primitive. It is shown that Godel already thought of that possibility in the Princeton lectures on intuitionism of Spring 1941, and evidence is presented that he adopted it in the same year or the next, long before the publication of 1958. Draft material for the revision of the Dialectica paper is discussed in which Godel describes the Dialectica Interpretation as being based on a new intuitionistic insight obtained by applying phenomenology, and also notes that relate the new notion of reductive proof to phenomenology. In an appendix, attention is drawn to notes from the archive according to which Godel anticipated autonomous transfinite progressions when writing his incompleteness paper. The principal topics are (1) personal contacts Godel had with Brouwer and Heyting; (2) various influences of intuitionism on Godel's work, in particular on the introduction of computable functional of finite type as a primitive notion; (3) archive material in which Godel describes the Dialectica Interpretation as based on an intuitionistic insight obtained by an application of phenomenology; (4) archive material around the notion of reductive proof and its relation to phenomenology; and, in an appendix, (5) archive material according to which Godel anticipated autonomous transfinite progressions when writing his incompleteness paper. A short companion paper describes archive material documenting the influence of Leibniz on the revision of the Dialectica paper (van Atten forthcoming).