The author gives a detailed quasi-complete review of Kawaguchi geometry of spaces obtained by the moving frame method, studied by himself in various previous papers. The review contains the main results concerning the geometry of the general type of Kawaguchi spaces together with their theoretical justification. It includes the global construction of special forms of the Cartan connection, in an arbitrary principal fibre bundle and their structural equation, also the global version of the Cartan-Laptev theorem on the structural equations of connections of the Cartan type. A description of the affine-normed structure of an arbitrary order is given. The review concludes with a study of Kawaguchi flat spaces.