While the LHC is entering the core of its activity, the high energy physics community is starting to outline the next generation of experiments. I will review the different ideas that have been proposed to continue the program of collider physics and highlight the physics cases and opportunities. I will discuss linear colliders such as the International Linear Collider (ILC) and the Compact LInear Collider (CLIC) and the Future Circular Collider (FCC-ee, FCC-hh) program. I will try to motivate, through several examples both of Standard Model measurements and new physics searches, the ongoing activity to identify the best candidate for a next generation collider. Focusing on some particularly motivated new physics frameworks, I will compare the expected sensitivity of lepton machines (ILC, CLIC, FCC-ee) in indirect measurements of Higgs properties, with the direct search capabilities of very high energy hadron machines (FCC-hh).