The controllability of coupled parabolic equations has been extensively studied these last two decades. We notice that some recent works highlighted new phenomena: existence of a positive minimal time for the null controllability and geometric conditions on the control domain. These phenomena, well-known in the case of the control of hyperbolic equations, was unexpected in the parabolic case. In this talk, we will study distributed and boundary controllability of two parabolic equations. We first give a necessary and sufficient condition of approximate controllability and then under some geometrical assumptions, the existence of a minimal time of null controllability is established. Finally, we show that we can reach any minimal time for boundary controllability.