%A H. Frankowska %T How Set-Valued Maps Pop Up in Control Theory %X We describe four instances where set-valued maps intervene either as a tool to state the results or as a technical tool of the proof. The paper is composed of four rather independent sections: (1) Set-Valued Optimal Synthesis and Differential Inclusions; (2) Viability Kernel; (3) Nonsmooth Solutions to Hamilton-Jacobi-Bellman Equations; (4) Interior and Boundary of Reachable Sets. %C IIASA, Laxenburg, Austria %D 1996 %I WP-96-116 %L iiasa4911