  The extended Linear Sigma Model (eLSM) is a hadronic model based on the
global symmetries of QCD and the corresponding explicit, anomalous, and
spontaneous breaking patterns. In its basic three-flavor form, its mesonic part
contains the dilaton/glueball as well as the nonets of (pseudo)scalar and
(axial-)vector mesons, thus chiral symmetry is linearly realized. In the chiral
limit and neglecting the chiral anomaly, only one term -- within the dilaton
potential -- breaks dilatation invariance. Spontaneous symmetry breaking is
implemented by a generalization of the Mexican-hat potential, with explicit
symmetry breaking responsible for its tilting. The overall mesonic
phenomenology up to 2 GeV is in agreement with the PDG compilation of masses
and decay widths. The eLSM was enlarged to include other conventional
quark-antiquark nonets (pseudovector and orbitally excited vector mesons,
(axial-)tensor mesons, etc.), as well as two nonets of hybrid mesons, the
lightest one with exotic quantum numbers $J^{PC} = 1^{-+}$ not allowed for
$\bar{q}q$ objects such as the resonance $\pi_1(1600)$ and the recently
discovered $\eta_1(1855)$. In doing so, different types of chiral multiplets
are introduced: heterochiral and homochiral multiplets, which differ in the way
they transform under chiral transformations. Moreover, besides the scalar
glueball, the tensor, the pseudoscalar and the vector glueballs were coupled to
the eLSM: the scalar $f_0(1710)$ turns out to be mostly gluonic, the tensor
glueball couples strongly to vector mesons, and the pseudoscalar glueball
couples can be assigned to $X(2370)$ or $X(2600)$. The eLSM contains chiral
partners on an equal footing and is therefore well suited for studies of chiral
symmetry restoration at nonzero temperature and densities. The QCD phase
diagram and the location of the critical endpoint were investigated within this
framework.
