The classical "art gallery problem" in computational geometry considers the following optimal coverage problem: Place a small number of points ("guards") in a geometric domain (e.g., polygon, or "art gallery") in order that every point of the domain is seen by one of the point guards. Many variants of the problem have been studied over the last few decades, both from the combinatorial perspective and from the algorithmic perspective. Given the obvious connection between guarding galleries and deploying sensors for good coverage in buildings, urban areas, etc, there has been a recent resurgence of interest in the classical art gallery problem. These geometric coverage problems give rise to a rich class of combinatorial optimization problems involving set cover problems with special structure. We discuss recent work we have done in devising and implementing heuristics and solving special cases with provable approximation bounds. We also discuss the closely related "watchman route problem", in which there is one or more mobile guard/sensor that is to perform optimal (minimum motion) coverage of a domain.