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 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.