Coverage control is a framework for effectively distributing a team of mobile robots over a domain of interest through coordinated control. Deploying real robots typically requires the consideration of their physical limitations and external constraints, such as connectivity maintenance or collision avoidance. This thesis investigates the incorporation of heterogeneous robot characteristics and various constraints into the coverage control framework. The most fundamental characteristic of a mobile robot is its mobility, which can also be seen as a constraint. This thesis begins with a coverage problem where a team of robots with different maximum speeds need to optimally cover a domain in terms of travel time. We then discuss how robots with different mobility types, e.g., ground and water, can perform coverage on a domain comprised of multiple terrain types while remaining in their compatible regions. In addition to mobility constraints, connectivity maintenance is crucial for coverage control, as it allows robots to collectively cover a domain through data sharing. Therefore, we examine how robots can establish and maintain a sparse communication network during coverage. Finally, we introduce a coverage control framework for aerial robots that effectively covers a given domain by balancing sensor resolution with the area of sensing and leveraging coverage redundancy.