General Introduction -- Fundamental Concepts, Definitions, and Models -- A Planar Percolation-Theoretic Approach to Coverage and Connectivity -- A Spatial Percolation-Theoretic Approach to Coverage and Connectivity -- A Planar Convexity Theory-Based Approach for Connected k-Coverage -- Planar Convexity Theory-Based Approaches for Heterogeneous, On-Demand, and Stochastic Connected k-Coverage -- Spatial Convexity Theory-Based Approaches for Connected k-Coverage.