Home delivery by drones as an alternative or complement to traditional delivery by trucks is attracting considerable attention from major retailers and service providers (Amazon, UPS, Google, DHL, Wal-mart, etc.), as well as several startups. While drone delivery may offer considerable economic savings, the fundamental issues of how best to deploy drones for home delivery are not well understood. Our research provides a strategic analysis for the design of hybrid truck-drone delivery systems using continuous approximation modeling techniques to derive general insights. We formulate and optimize models of hybrid truck-drone delivery, where truck-based drones make deliveries simultaneously with trucks, and compare their performance to truck-only delivery. Our results suggest that truck-drone delivery can be very advantageous economically in many settings, especially with multiple drones per truck, but that the benefits depend strongly on the relative operating costs and marginal stop costs.