Mobile robots are used in a broad range of application areas; e.g. search and rescue, reconnaissance, exploration, etc. Given the increasing need for high performance mobile robots, the area has received attention by researchers. In this thesis, critical control and control-relevant design issues for differential drive mobile robots is addressed. Two major themes that have been explored are the use of kinematic models for control design and the use of decentralized proportional plus integral (PI) control. While these topics have received much attention, there still remain critical questions which have not been rigorously addressed. In this thesis, answers to the following critical questions are provided: When is 1. a kinematic model sufficient for control design? 2. coupled dynamics essential? 3. a decentralized PI inner loop velocity controller sufficient? 4. centralized multiple-input multiple-output (MIMO) control essential? and how can one design the robot to relax the requirements implied in 1 and 2? In this thesis, the following is shown: 1. The nonlinear kinematic model will suffice for control design when the inner velocity (dynamic) loop is much faster (10X) than the slower outer positioning loop. 2. A dynamic model is essential when the inner velocity (dynamic) loop is less than two times faster than the slower outer positioning loop. 3. A decentralized inner loop PI velocity controller will be sufficient for accomplish- ing high performance control when the required velocity bandwidth is small, rel- ative to the peak dynamic coupling frequency. A rule-of-thumb which depends on the robot aspect ratio is given. 4. A centralized MIMO velocity controller is needed when the required bandwidth is large, relative to the peak dynamic coupling frequency. Here, the analysis in the thesis is sparse making the topic an area for future analytical work. Despite this, it is clearly shown that a centralized MIMO inner loop controller can offer increased performance vis- ́a-vis a decentralized PI controller. 5. Finally, it is shown how the dynamic coupling depends on the robot aspect ratio and how the coupling can be significantly reduced. As such, this can be used to ease the requirements imposed by 2 and 4 above.