Looking for associations among multiple variables is a topical issue in statistics due to the increasing amount of data encountered in biology, medicine, and many other domains involving statistical applications. Graphical models have recently gained popularity for this purpose in the statistical literature. In the binary case, however, exact inference is generally very slow or even intractable because of the form of the so-called log-partition function. In this paper, we review various approximate methods for structure selection in binary graphical models that have recently been proposed in the literature and compare them through an extensive simulation study. We also propose a modification of one existing method, that is shown to achieve good performance and to be generally very fast. We conclude with an application in which we search for associations among causes of death recorded on French death certificates.