Using the fixed point approach many different problems in control theory are studied. Several results concerning controllability, observability, parameter estimation and adaptive regulation for the so called ``semilinear'' dynamical systems are presented. All the results described make use of the various types of fixed point theorems. The importance of the fixed point approach lies in its constructive aspects. Most of the results are formulated for infinite-dimensional semilinear control systems. Several remarks, comments and relationships between different results are presented. Similar problems have been considered in the papers by the reviewer [Automatica 12, 633-634 (1976; Zbl 0345.93014); Int. J. Control 31, 911- 919 (1980; Zbl 0462.93009)], and by \textit{Y. Yamamoto} [J. Optimization Theory Appl. 22, 41-49 (1977; Zbl 0353.93013)].