The mismatch between the extensive clinical use of deep brain stimulation (DBS), which is being used to treat an increasing number of neurological disorders, and the lack of understanding of the underlying mechanisms is confounded by the difficulty of measuring the spread of electric current in the brain in vivo. In this article we present a brief review of the recent computational models that simulate the electric current and field distribution in 3D space and, consequently, make estimations of the brain volume being modulated by therapeutic DBS. Such structural modeling work can be categorized into three main approaches: target-specific modeling, models of instrumentation and modeling the electrode-brain interface. Comments are made for each of these approaches with emphasis on our electrode-brain interface modeling, since the stimulating current must travel across the electrode-brain interface in order to reach the surrounding brain tissue and modulate the pathological neural activity. For future modeling work, a combined approach needs to be taken to reveal the underlying mechanisms, and both structural and dynamic models need to be clinically validated to make reliable predictions about the therapeutic effect of DBS in order to assist clinical practice.