  Gaussian graphical models provide a powerful framework to reveal the
conditional dependency structure between multivariate variables. The process of
uncovering the conditional dependency network is known as structure learning.
Bayesian methods can measure the uncertainty of conditional relationships and
include prior information. However, frequentist methods are often preferred due
to the computational burden of the Bayesian approach. Over the last decade,
Bayesian methods have seen substantial improvements, with some now capable of
generating accurate estimates of graphs up to a thousand variables in mere
minutes. Despite these advancements, a comprehensive review or empirical
comparison of all recent methods has not been conducted. This paper delves into
a wide spectrum of Bayesian approaches used for structure learning and
evaluates their efficacy through a comprehensive simulation study. We also
demonstrate how to apply Bayesian structure learning to a real-world data set
and provide directions for future research. This study gives an exhaustive
overview of this dynamic field for newcomers, practitioners, and experts.
