Linear, finite-dimensional, continuous-time, stochastic control systems with time-varying parameters are considered. Fundamental definitions of stochastic controllability are presented. Next, using the theory of stochastic differential equations, methods of functional analysis and the minimum energy principle, many conditions for complete controllability, approximate controllability and stochastic controllability are formulated and proved. The rank conditions for different kinds of controllability are also given. Moreover, many remarks and comments concerning stochastic controllability and its relations to other concepts of controllability are pointed out. Finally, it should be stressed that similar stochastic controllability problems were considered in the paper [

*J. Klamka* and

*L. Socha*, IEEE Trans. Autom. Control 22, 880-881 (1977;

Zbl 0363.93048)].