Robot person following (RPF)---mobile robots that follow and assist a specific person---has emerging applications in personal assistance, security patrols, eldercare, and logistics. To be effective, such robots must accompany the target while ensuring both safety and comfort for the target and surrounding people. In this work, we present the first end-to-end study of RPF, which (i) surveys representative scenarios, motion-planning methods, and evaluation metrics with a focus on safety and comfort; (ii) introduces Follow-Bench, a unified benchmark that simulates diverse scenarios, including various target trajectory patters, dynamic-crowd patterns, and topographical variations; and (iii) re-implements six popular RPF planners, ensuring that both safety and comfort are systematically considered. Moreover, we evaluate the two highest-performing planners from our benchmark on a differential-drive robot to provide insights into real-world deployment. Extensive simulation and real-world experiments provide quantitative insights into the safety-comfort trade-offs of existing planners, while revealing open challenges and future research directions.