What currently limits charge carrier mobility in crystals of molecular semiconductors?

Charge carrier mobility is a central property that characterizes the performances of organic semiconductors and is mostly measured in field-effect transistors. High mobility values are sought by many research teams. This article, that provides an overview of best performing molecular semiconductors is constructed on the question: What currently limits charge carrier mobility in crystals of molecular semiconductors? With this in mind, we confront, in a critical way, the current theoretical understanding to the most salient experimental results with the hope to reach a deeper understanding based on first principles and order of magnitudes of the main physical parameters.