Flagella and cilia are slender structures that serve important functionalities in the microscopic world through their locomotion induced by fluid and structure interaction. With recent developments in microscopy, fabrication, biology, and modeling capability, robots inspired by the locomotion of these organelles in low Reynolds number flow have been manufactured and tested on the micro-and macro-scale, ranging from medical in vivo microbots, microfluidics to macro prototypes. We present an unprecedented collection of modeling theories, control principles, and fabrication methods for flagellated and ciliary robots.