Over the past decade, there has been considerable interest in miniaturizing aircraft to create a class of extremely small, robotic vehicles with a gross mass on the order of tens of grams and a dimension on the order of tens of centimeters. These are collectively refered to as micro aerial vehicles (MAVs) or microflyers. Because the size of microflyers is on the same order as that of small birds and large insects, engineers are turning to nature for inspiration. Bioinspired concepts make use of structural or aerodynamic mechanisms that are observed in insects and birds, such as elastic energy storage and unsteady aerodynamics. Biomimetic concepts attempt to replicate the form and function of natural flyers, such as flapping-wing propulsion and external appearance. This paper reviews recent developments in the area of man-made microflyers. The design space for microflyers will be described, along with fundamental physical limits to miniaturization. Key aerodynamic phenomena at the scale of microflyers will be highlighted. Because the focus is on bioinspiration and biomimetics, scaled-down versions of conventional aircraft, such as fixed wing micro air vehicles and microhelicopters will not be addressed. A few representative bioinspired and biomimetic microflyer concepts developed by researchers will be described in detail. Finally, some of the sensing mechanisms used by natural flyers that are being implemented in man-made microflyers will be discussed.