The fascinating properties of ionic liquids, their versatility for different applications and their highly non-ideal behavior have promoted the study of these systems from different perspectives. This article provides an overview of the different approaches that have been applied to describe the thermodynamic behavior of ionic liquids and the solubility of selected compounds in them, including carbon dioxide, hydrogen, water, BF3 and other compounds. The paper deals with some of the most recent and refined approaches involving physical models developed to characterize the ionic liquids. Emphasis is put on the models based on statistical mechanics, highlighting the advantages of these models versus classical ones. New modeling results involving the chemical association of BF3 in ionic liquids and interfacial properties of selected ionic liquids within the framework of soft-SAFT are also presented. It is seen that the great advance in the refined modeling tools allows not only quantitative agreement with known experimental data, but also a guide to some of the physics governing the behavior of these systems, a step forward into developing ad hoc ionic liquids for specific applications. (C) 2010 Published by Elsevier B.V.