The problem of learning\ the Markov network structure\ from data\ has become increasingly important in machine learning,

and in many other application fields.\ Markov networks are probabilistic graphical models,\ a widely used formalism for handling probability distributions in intelligent systems.\ This document focuses on a technology called \emph{independence-based} learning,\ which allows for the learning of the independence structure of Markov networks from data in an efficient and sound manner,\ whenever the dataset is sufficiently large, and data is a representative sample of the target distribution.\ In the analysis of such technology, this work surveys the current state-of-the-art algorithms,\ discussing its limitations, and posing a series of open problems\ where future work may produce some advances in the area, in terms of quality and efficiency.