  In this paper we summarise the constraints that low-redshift data --such as
supernovae Ia (SN Ia), baryon acoustic oscillations (BAO) and cosmic
chronometers (CC)-- are able to set on the concordance model and its
extensions, as well as on inhomogeneous but isotropic models. We provide a
broad overlook into these cosmological scenarios and several aspects of data
analysis. In particular, we review a number of systematic issues of SN Ia
analysis that include magnitude correction techniques, selection bias and their
influence on the inferred cosmological constraints. Furthermore, we examine the
isotropic and anisotropic components of the BAO data and their individual
relevance for cosmological model-fitting. We extend the discussion presented in
earlier works regarding the inferred dynamics of cosmic expansion and its
present rate from the low-redshift data. Specifically, we discuss the
cosmological constraints on the accelerated expansion and related
model-selections. In addition, we extensively talk about the Hubble constant
problem, then focus on the low-redshift data constraint on $H_0$ that is based
on CC. Finally, we present the way in which this result compares the two of
high-redshift $H_0$ estimate and local (redshift zero) measurements that are in
tension.
