Due to labor shortage and rising labor cost for the apple industry, there is an urgent need for the development of robotic systems to efficiently and autonomously harvest apples. In this paper, we present a system overview and algorithm design of our recently developed robotic apple harvester prototype. Our robotic system is enabled by the close integration of several core modules, including visual perception, planning, and control. This paper covers the main methods and advancements in deep learning-based multi-view fruit detection and localization, unified picking and dropping planning, and dexterous manipulation control. Indoor and field experiments were conducted to evaluate the performance of the developed system, which achieved an average picking rate of 3.6 seconds per apple. This is a significant improvement over other reported apple harvesting robots with a picking rate in the range of 7-10 seconds per apple. The current prototype shows promising performance towards further development of efficient and automated apple harvesting technology. Finally, limitations of the current system and future work are discussed.