1) Embedded computing systems are programmable computers designed for specialized applications rather than general-purpose use. They are found in devices like cell phones, cars, appliances. 2) Early embedded systems date to the 1940s but microprocessors enabled more complex embedded applications starting in the 1970s. Modern vehicles can have over 100 microprocessors controlling various functions. 3) Embedded system design faces challenges like meeting deadlines, minimizing power consumption, and tight design timelines with small teams. Methodical design processes help address these challenges.