The Two Higgs Doublet Model (2HDM) is a simple extension of the Standard Model (SM), which
provides a rich and very interesting phenomenology. To remove the undesirable flavour-changing
neutral currents (FCNCs), an additional $\mathcal Z_2$ symmetry is usually imposed into the 2HDM. However,
FCNCs can be avoided in a much more general way by assuming a similar Yukawa structure for
the two scalar doublets. The model with this intriguing feature is termed the Aligned Two Higgs
Doublet Model (A2HDM). The phenomenological constraints on the A2HDM are much weaker
than the ones on the usual $\mathcal Z_2$ models, opening a broader range of possible scenarios. Moreover,
the A2HDM also provides a generic framework to study, as particular cases, the different varieties
of $\mathcal Z_2$-symmetric 2HDMs. Here, we illustrate a global fit of the A2HDM using the package
HEPfit. We study the possibility of having new scalar particles lighter than the SM Higgs. For this
global fit we perform a Bayesian analysis, including stability and perturbativity bounds, flavour
and electroweak precision observables, and scalar (and pseudoscalar) searches at LEP and LHC.