The effectiveness of drug combinations for treatment of a variety of complex diseases is well established. "Drug cocktail" treatments are often prescribed to improve the overall efficacy, decrease toxicity, alter pharmacodynamics, etc in an overall treatment strategy. Specifically, if when combined, drugs interact in some way that causes the total effect to be greater than that predicted by their individual potencies, then drugs are considered synergistic. While there are established ways to quantify the impact of drug combinations clinically, it is an open challenge to quantitatively summarize a synergistic interaction. In this paper, we discuss an overview of the current statistical and mathematical methods for the study of drug combination effects, especially drug synergy quantification (where the interaction effect is not just detected, but quantified according to its magnitude). We first introduce two popular reference models for testing to null hypothesis of non-interaction for a combination, including the Bliss independence model and the Loewe additivity model. Then we discuss several methods for quantifying drug synergism. The advantages and disadvantages with these methods are also provided, and finally, we discuss important next directions in this area.