The Electron Ion Collider is preparing now the design for the project baseline, to provide the high luminosity, polarization and flexibility for the EIC. This talk outlines the accelerator physics challenges including complex interaction region, flat hadron beams, beam cooling, high beam currents leading possibly to electron clouds and instabilities, and high beam polarization.

A lepton-collider Higgs factory, to precisely measure the couplings of the Higgs boson to other particles, followed by a higher energy run to measure the Higgs self-coupling, is widely recognized as a primary focus of modern particle physics. In the talk a description of the new technology based on cool copper that can lead to compact and affordable machine will be described as well as the issues and challenges of this type of technology.