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This contribution outlines the HALHF concept, which combines the highgradients achievable in plasma-wakefield acceleration with conventionalradio-frequency acceleration. In HALHF, beam-driven plasma-wakefield cells areused to accelerate electrons to high energy. Because plasma-based accelerationof positrons is problematic, conventional RF acceleration is used but to muchlower energy. The HALHF concept utilises not only asymmetric energies but alsoasymmetric bunch charges and asymmetric transverse emittances, leading tocomparable luminosity to conventional facilities but much lower capital cost.Possible upgrades to the HALHF facility are discussed, in particular to the$\rm{t\bar{t}}$ threshold and to 550 GeV, where the Higgs self-coupling and$\rm{t\bar{t}}H$ coupling can be measured. Other upgrades include the provisionof two interaction points, to implement a $\gamma$$\unicode{x2013}$$\gamma$collider of two possible types and finally a symmetric high-energy collider ifthe problem of plasma-based positron acceleration can be solved.

Status of and upgrade concepts for HALHF: the hybrid, asymmetric, linear Higgs factory