  The description of strong interaction physics of low-lying resonances is out
of the valid range of perturbative QCD. Chiral effective field theories have
been developed to tackle the issue. Partial wave dynamics is the systematic
tool to decode the underlying physics and reveal the properties of those
resonances. It is extremely powerful and helpful for our understanding of the
non-perturbative regime, especially when dispersion techniques are utilized
simultaneously. Recently, plenty of exotic/ordinary hadrons have been reported
by experiment collaborations, e.g. LHCb, Belle, and BESIII, etc.. In this
review, we summarize the recent progress on the applications of partial wave
dynamics combined with chiral effective field theories and dispersion
relations, on related topics, with emphasis on $\pi\pi$, $\pi K$, $\pi N$ and
$\bar{K}N$ scatterings.
