Indications for extra scalars at LHC? -- BSM physics at future $e^+e^-$ colliders

This paper intends to collect available data on searches for scalar resonances at LHC. It is suggested that in the absence of SUSY, the most compelling picture is the composite framework, with the idea that the lightest particles are composite scalars of the pseudo-Nambu-Goldstone type, emerging from a broken symmetry at a higher scale, the h(125) boson being one of them. Searches in two-photons, Z-photon, ZZ into 4 leptons, top, h(125) and W pairs are reviewed. Aside from the already well-known scalar observed by CMS and LEP2 at 96 GeV, I discuss the evidence and the interpretation for a possible resonance observed in ZZ around 700 GeV by CMS and ATLAS and some evidence for a CP-odd scalar at 440 GeV. Future searches at HL-LHC and at future $e^+e^-$ colliders are briefly sketched