  Quantum Chromodynamics constitutes the quantum field theory of the strong
interaction. Despite the success of this theory in the description of several
hadronic processes, the elastic scattering is still a theoretical challenge.
This process is characterized by a small transferred momentum and the
perturbative techniques are not applicable. Although nonperturbative results
have been obtained in recent years, we still do not have a full description
within QCD of the quantities related to the elastic scattering, for example,
$\sigma_{tot}$, the $\rho$ parameter and $\sigma_{el}$. In this thesis, the
main interest is in the energy dependence of the ratio
$X=\sigma_{el}/\sigma_{tot}$, $\sigma_{tot}$ and $\rho$. These topics are
divided into three different studies. In the first topic, we develop an
empirical analysis on the ratio $X$. By means of parameterizations with a small
number of free parameters, we have obtained good descriptions of the data on
$pp$ and $\bar{p}p$ scattering. We conclude that the asymptotic black-disk
scenario is not a unique solution and the results favour a grey-disk scenario.
In the second topic, we study the rise of $\sigma_{tot}$ with the energy
through parameterizations based on the Regge-Gribov formalism and we consider
two options for the leading term: a log-square and a log-raised-to-$\gamma$,
with $\gamma$ a free fit parameter. We discuss two analytic methods to connect
the real and imaginary parts of the amplitude: Derivative Dispersion Relations
(DDR) and Asymptotic Uniqueness, which lead to different parameterizations for
$\sigma_{tot}$ and $\rho$. The results favour the DDR method in both formal and
practical contexts. In the third topic, two sub-leading terms for
$\sigma_{tot}$, obtained in a nonperturbative QCD approach, are considered in
fits to $pp$ and $\bar{p}p$ data and also in fits to data from meson-baryon and
other baryon-baryon scattering.
