Most real life bubble dynamics applications involve multiple bubbles, for example, in cavitation erosion prevention, ultrasonic baths, underwater warfare, and medical applications involving microbubble contrast agents. Most scientific dealings with bubble-bubble interaction focus on two similarly sized bubbles. In this study, the interaction between two oscillating differently sized bubbles (generated in tap water) is studied using high speed photography. Four types of bubble behavior were observed, namely, jetting toward each other, jetting away from each other, bubble coalescence, and a behavior termed the "catapult" effect. In-phase bubbles jet toward each other, while out-of-phase bubbles jet away from each other. There exists a critical phase difference that separates the two regimes. The behavior of the bubbles is fully characterized by their dimensionless separation distance, their phase difference, and their size ratio. It is also found that for bubbles with large size difference, the smaller bubble behaves similarly to a single bubble oscillating near a free surface.