  The problem of reproducing dark energy effects is reviewed here with
particular interest devoted to cosmography. We summarize some of the most
relevant cosmological models, based on the assumption that the corresponding
barotropic equations of state evolve as the universe expands, giving rise to
the accelerated expansion. We describe in detail the $\Lambda$CDM
($\Lambda$-Cold Dark Matter) and $\omega$CDM models, considering also some
specific examples, e.g., Chevallier-Polarsky-Linder, the Chaplygin gas and the
Dvali-Gabadadze-Porrati cosmological model. Finally, we consider the
cosmological consequences of $f(\mathcal{R})$ and $f(\mathcal{T})$ gravities
and their impact on the framework of cosmography. Keeping these considerations
in mind, we point out the \emph{model-independent} procedure related to
cosmography, showing how to match the series of cosmological observables to the
free parameters of each model. We critically discuss the role played by
cosmography, as a \emph{selection criterion} to check whether a particular
model passes or does not present cosmological constraints. In so doing, we find
out cosmological bounds by fitting the luminosity distance expansion of the
redshift, z, adopting the recent Union 2.1 dataset of supernovae, combined with
the baryonic acoustic oscillation and the cosmic microwave background
measurements. We perform cosmographic analyses, imposing different priors on
the Hubble rate present value. In addition, we compare our results with recent
PLANCK limits, showing that the $\Lambda$CDM and $\omega$CDM models seem to be
the favorite with respect to other dark energy models. However, we show that
cosmographic constraints on $f(\mathcal{R})$ and $f(\mathcal{T})$ cannot
discriminate between extensions of General Relativity and dark energy models,
leading to a disadvantageous degeneracy problem.
