  Measurements of the Higgs boson production times decay rates and differential
cross-sections have recently been performed by the ATLAS experiment in several
decay channels using up to 139 fb$^{-1}$ of proton-proton collision data at
$\sqrt{s}=13$ TeV recorded at the Large Hadron Collider. This paper presents
multiple interpretations of these Higgs boson measurements. Measurements of
production-mode cross-sections, simplified template cross-sections and fiducial
differential cross-sections in different decay channels are reparameterised in
terms of the impact of Standard Model effective field theory operators, and
constraints are reported on the corresponding Wilson coefficients. Production
and decay rate measurements are interpreted in UV-complete extensions of the
Standard Model, namely the two-Higgs-doublet model (2HDM) near thealignment
limit and the Minimal Supersymmetric Standard Model (MSSM) for various MSSM
benchmark scenarios. The constraints on the 2HDM parameters
$(\cos(\beta-\alpha), \tan\beta)$ and the MSSM parameters $(m_A, \tan\beta)$
are complementary to those obtained from direct searches for additional Higgs
bosons.
