Freehand three-dimensional ultrasound (3D-US) has gained considerable interest in research, but even today suffers from its high inter-operator variability in clinical practice. The high variability mainly arises from tracking inaccuracies as well as the directionality of the ultrasound data, being neglected in most of today's reconstruction methods. By providing a novel paradigm for the acquisition and reconstruction of tracked freehand 3D ultrasound, this work presents the concept of Computational Sonography (CS) to model the directionality of ultrasound information. CS preserves the directionality of the acquired data, and allows for its exploitation by computational algorithms. In this regard, we propose a set of mathematical models to represent 3D-US data, inspired by the physics of ultrasound imaging. We compare different models of Computational Sonography to classical scalar compounding for freehand acquisitions, providing both an improved preservation of US directionality as well as improved image quality in 3D. The novel concept is evaluated for a set of phantom datasets, as well as for in-vivo acquisitions of muscoloskeletal and vascular applications.