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.