High energy particle colliders have been in the forefront of particle physics for more than three decades. At present the near term US, European and international strategies of the particle physics community are centered on full exploitation of the physics potential of the Large Hadron Collider (LHC) through its high-luminosity upgrade (HL-LHC). The future of the world-wide HEP community critically depends on the feasibility of possible post-LHC colliders. The concept of the feasibility is complex and includes at least three factors: feasibility of energy, feasibility of luminosity and feasibility of cost. Here we overview all current options for post-LHC colliders from such perspective (ILC, CLIC, Muon Collider, plasma colliders, CEPC, FCC, HE-LHC) and discuss major challenges and accelerator R&D required to demonstrate feasibility of an energy frontier accelerator facility following the LHC. We conclude by taking a look into ultimate energy reach accelerators based on plasmas and crystals, and discussion on the perspectives for the far future of the accelerator-based particle physics.