  In this paper, we discuss our recent works on the null-controllability, the
exact controllability, and the stabilization of linear hyperbolic systems in
one dimensional space using boundary controls on one side for the optimal time.
Under precise and generic assumptions on the boundary conditions on the other
side, we first obtain the optimal time for the null and the exact
controllability for these systems for a generic source term. We then prove the
null-controllability and the exact controllability for any time greater than
the optimal time and for any source term. Finally, for homogeneous systems, we
design feedbacks which stabilize the systems and bring them to the zero state
at the optimal time. Extensions for the non-linear homogeneous system are also
discussed
