  This work reports the most relevant technical aspects in the problem of
learning the \emph{Markov network structure} from data. Such problem has become
increasingly important in machine learning, and many other application fields
of machine learning. Markov networks, together with Bayesian networks, are
probabilistic graphical models, a widely used formalism for handling
probability distributions in intelligent systems. Learning graphical models
from data have been extensively applied for the case of Bayesian networks, but
for Markov networks learning it is not tractable in practice. However, this
situation is changing with time, given the exponential growth of computers
capacity, the plethora of available digital data, and the researching on new
learning technologies. This work stresses on a technology called
independence-based learning, which allows the learning of the independence
structure of those networks from data in an efficient and sound manner,
whenever the dataset is sufficiently large, and data is a representative
sampling of the target distribution. In the analysis of such technology, this
work surveys the current state-of-the-art algorithms for learning Markov
networks structure, discussing its current limitations, and proposing a series
of open problems where future works may produce some advances in the area in
terms of quality and efficiency. The paper concludes by opening a discussion
about how to develop a general formalism for improving the quality of the
structures learned, when data is scarce.
