In this talk, we are concerned with minimal control time for 1D linear hyperbolic systems of balance laws. We will show how such critical quantities depend on internal and boundary couplings under various types of controllability (exact controllability (EC), null-controllability (NC), boundary controllability (BC) and internal controllability (IC)). A key aspect will be demonstrated that the minimal time can be strictly smaller than the classical one proposed by J.-M. Coron, T.T. Li and D. Russell etc. Moreover, the difference between EC and NC and equivalence between BC and IC will also be highlighted. This talk is based on recent joint works with Guillaume Olive.