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Plasma-wakefield acceleration promises orders of magnitude higher gradients than can be achieved via conventional radio-frequency cavities. It is now starting to be used in real user facilities. However, its application to particle-physics colliders has always been complicated by the difficulty in accelerating positrons. I will introduce the basics of plasma wakefield acceleration and explain the difficulty with accelerating positrons. HALHF avoids this by using a conventional linac to accelerate positrons, resulting in an asymmetric-energy, hybrid linear facility which is much smaller, greener and cheaper than any conventional alternative Higgs-factory proposal. I will outline the HALHF layout and principles, possible upgrades to the Higgs factory and the R&D path to making it a reality.