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.