This is a survey paper on some research in the field of control and differential games, performed by the author and his scientific school. The first part is devoted to duality between control and observation for linear time-varying continuous-time systems. The second part relates to differential games in mixed strategies. The references given are to monographs by the author and his colleagues A. B. Kurzhanskiĭ, A. N. Krasovskiĭ, and A. I. Subbotin.