  We discuss some topics concerning rational approximations in Quantum
Chromodynamics, especially those related with the mathematical theory of Pad\'e
Approximants. We focus on two kind of problems: the first one related with
meromorphic functions (inspired by the Large-Nc limit in QCD) where we explore
the Minimal Hadronic Approximation through the extraction of Low-Energy
Constants and Condensate parameters of a two-point Green's function; and the
second one related with meromorphic functions of Stieltjes-type where we
present a critical analysis to a unitarization process applied to the Linear
Sigma Model and also and application of the Pad\'e Theory to the vacuum
polarization function of a heavy quark. We also show the ability of these
approximations when working with experimental data. Along these line, we make
special emphasis on the reliability of that theory to control on systematic
errors.
