I will discuss some theoretical and phenomenological aspects of the off-shell Higgs physics based on 1903.07725. The question ``How does the Higgs boson propagate?'' is framed in the context of Universal effective field theories. The Higgs boson oblique parameter H is introduced; consistency conditions stemming from Kallen-Lehmann representation are derived; examples of UV completions are provided. Finally, the four-top production is advertised as an effective high-energy probe of off-shell Higgs behaviour.