Approximate dynamic programming (ADP) has been widely studied from several important perspectives: algorithm development, learning efficiency measured by success or failure statistics, convergence rate, and learning error bounds. Given that many learning benchmarks used in ADP or reinforcement learning studies are control problems, it is important and necessary to examine the learning controllers from a control-theoretic perspective. This paper makes use of direct heuristic dynamic programming (direct HDP) and several benchmark examples to introduce a unique analytical framework that can be extended to other learning control paradigms and other complex control problems. The sensitivity analysis and the linear quadratic regulator (LQR) design are used in the paper for two purposes: to gauge direct HDP performance characteristics and to provide guidance toward designing better learning controllers. This gauge however does not limit the direct HDP to be effective only as a linear controller. Toward this end, applications of the direct HDP for nonlinear control problems beyond sensitivity analysis and the confines of LQR have been developed and compared with LQR design for command following and internal system parameter changes.