Let's sort the foundations a bit.
The fundamental theory describing the strong interactions is quantum chromodynamics (QCD). It's fundamental symmetry is the local color-charge group ##\mathrm{SU}(3)_{\text{col}}##. The fields in the Lagrangian are the 6 quark flavors, which are represented by Dirac fields and the color-gauge fields, the gluons. The remarkable feature of QCD is its asymptotic freedom, i.e., the running coupling in renormalized perturbation theory gets small for the large energy-momentum scales, i.e., for high-energy scattering events.
At low energies, we cannot observe quarks and gluons as asymptotic free states. The reason is called confinement. The asymptotic free states observed are the colorless hadrons (mesons made of a quark and an antiquark and baryons made of three quarks; there are also hints for "exotic" configurations like tetra quark states). Confinement cannot be described in the realm of perturbation thery, but there are very convincing results from lattice QCD, where QCD is evaluated non-perturbatively on a space-time grid on a computer, and the observed mass spectrum of hadrons is reproduced very well nowadays.
So at low energies the relevant degrees of freedom are hadrons, and thus one has to use effective field theories for them. Now the question is, how to model these interactions, and there nature is kind to us in providing more symmetries of the QCD Lagrangian than the fundamental local color symmetry. These are global ("ungauged") symmetries. The most important one in the light-quark sector (u- and d-quarks) is chiral symmetry. Compared to typical scales of the light hadrons (around 1 GeV) the current-quark masses of the light quarks with only some MeV (inferred from deep inelastic scattering, where perturbative QCD is applicable) are small. So you can first consider the limit, where you set these quark masses to 0. Then the u and d quark interaction in QCD becomes symmetric under chiral transformations, i.e., you can rotate the left- and the right-handed part of the corresponding Dirac spinors with independent SU(2) rotations in flavor space. This is the ##\mathrm{SU}(2)_L \otimes \mathrm{SU}(2)_R## symmetry.
Now the strong interaction leads to spontaneous breaking of this symmetry, i.e., the ground state is not symmetric under this group. The reason is that the vacuum expectation value (vev) of the quark condensate ##\langle \overline{\psi} \psi \rangle \neq 0##. This breaks the chiral symmetry such that only the part of the symmetry which keeps the quark-condensate vev invariant, and that's the vector part of this group, the ##\mathrm{SU}(2)_V##, the isospin rotations. So from the originally 6-dimensional group parameters you are left with only 3. Goldstone's theorem now tells you that thus there must be 3 massless pseudoscalar states, and these are identified with the pions, because those are very light (##m_{\pi} \simeq 140 \; \mathrm{MeV}##).
In this chiral limit, thus you can argue as follows: We build a Lagrangian for scalar bosons with chiral symmetry and break this symmetry spontaneously to the ##\mathrm{SU}(2)_V## such that you get three massless pseudoscalar bosons which you identify with the pions. The most simple example is the linear ##\sigma## model, invented by Gell-Mann and Levy in 1960. You realize the chiral symmetry as an ##\mathrm{SO}(4)## acting on a quartet of real fields ##\vec{\phi}## and write a mass term with the wrong sign and a symmetric four-field coupling
$$\mathcal{L}=\frac{1}{2} (\partial_{\mu} \vec{\phi}) \cdot (\partial_{\mu} \vec{\phi} ) + \frac{\mu^2}{2} \vec{\phi}^2 - \frac{\lambda}{8} (\vec{\phi} \cdot \vec{\phi})^4.$$
The ground state is not at ##\vec{\phi}=0##, because the potential has no minimum there. You can now choose the direction of the thus needed vev for the fields ##\vec{\phi}## arbitrarily (the ground state for a spontaneously broken global symmetry is always degenerate!), e.g., ##\langle \vec{\phi} \rangle=(\sigma_0,0,0,0)##. Then the rotations of the last three components leave the vacuum unchanged and rotations in a plane containing a component in the first direction don't. Thus rewriting the Lagrangian by setting ##\vec{\phi}=(\sigma_0+\sigma, \vec{\pi})##, you'll find that the three ##\vec{\pi}## field degrees of freedom represent massless particles, the Goldstone bosons of the spontaneously broken symmetry, and you are left with another scalar boson, represented by ##\sigma##, it's known as the ##\sigma## meson or in the more modern naming scheme as the ##f_0##. It is a very broad resonance with a mass between 400-550 MeV and a width of 400-700 MeV.
Now the chiral symmetry is only approximate, because the u- and d-quarks are not exactly massless but have a small mass of some MeV. Thus the pion becomes massive, and one has to add a small symmetry-breaking term in the effective Lagrangian. Since it's small it can be treated as a perturbation ("chiral perturbation theory"). If the u- and the d-quark masses were equal the isospin symmetry would be still exact, but it's also already violated by the difference of the quark masses, but it's still a pretty good approximate theory.
Now, if you add the electromagnetic interaction to the game, the isospin symmetry is also broken by this, but again it's only a small breaking, because the em. interaction is so weak.
Phenomenologically the socalled vector-meson dominance model is quite successful to describe the electromagnetic interactions of hadrons. It is based on the assumption that the electromagnetic current is proportional to the (charge neutral) light-vector meson fields (##\rho##, ##\omega## and if you add strangeness also ##\phi##). These are massive vector fields. If you take only the charge-neutral vector mesons you can make a abelian gauge model with massive gauge bosons. There's nothing forbidding naively added mass terms to the gauge fields for an Abelian U(1) gauge group (Stueckelberg formalism). The theory is still gauge invariant (and in minimal-coupling form even renormalizable). It's like QED with a massive photon, but now describing the strong interaction among vector mesons and pions.
Of course, one is also interested in describing all the vector mesons, not only the uncharged. The ##\rho## meson, e.g., is a isovector meson and comes thus as three such mesons, one neutral and one positively and one negatively charged. Then you'd like to describe this as a SU(3) gauge theory, which is non-abelian. This has indeed been done by Bando, Kugo at al in the mid 1980ies: You take an additional "hidden" gauge group (one does NOT gauge the chiral symmetry, because then the pions would get eaten up as the third degree of freedom of the then massive ##\rho## mesons when Higgsing it).
As in the standard model of the electroweak interaction you'd end up with an additional massive Higgs boson in the physical particle spectrum. Since this is unwanted, one integrates this out by realizing the hidden-local symmetry non-linearly, i.e., without a Higgs boson. This is then of course no longer renormalizable, but that doesn't matter, because one sees it anyway as a low-energy representation, i.e., an effective field theory, which has to be expanded in powers of momentum and thus carries infinitely many low-energy constants. The only constraint are the underlying symmetries. The same is true of the chiral perturbation theory describing hadrons.
