This volume is an outcome of the conference ``Geometry and Foliations 2013'', held in Tokyo in September 2013, and associated meetings. The volume aims to provide a good overview of present studies as well as some perspective for further studies. It includes B. Deroin's survey on Brownian motions on foliated complex surfaces, which contains many essential results and ideas. Other articles cover a wide range of topics related to foliations and groups of diffeomorphisms old and new; some articles discuss characteristic classes such as Godbillon-Vey class or homotopy theory of foliations while others deal with topological and differential geometrical aspects, particularly in the holomorphic setting. Several articles show the relationship of these topics to geometric group theory. This volume is highly recommended to researchers and graduate students interested in the theories of foliations and related topics such as diffeomorphism groups and geometric group theory.