Optical metasurfaces, capable of manipulating the properties of light with a thickness at the subwavelength scale, have been the subject of extensive investigation in recent decades. This research has been mainly driven by their potential to overcome the limitations of traditional, bulky optical devices. However, most existing optical metasurfaces are confined to planar and rigid designs, functions, and technologies, which greatly impede their evolution toward practical applications that often involve complex surfaces. The disconnect between two-dimensional (2D) planar structures and three-dimensional (3D) curved surfaces is becoming increasingly pronounced. In the past two decades, the emergence of flexible electronics has ushered in an emerging era for metasurfaces. This review delves into this cutting-edge field, with a focus on both flexible and conformal design and fabrication techniques. Initially, we reflect on the milestones and trajectories in modern research of optical metasurfaces, complemented by a brief overview of their theoretical underpinnings and primary classifications. We then showcase four advanced applications of optical metasurfaces, emphasizing their promising prospects and relevance in areas such as imaging, biosensing, cloaking, and multifunctionality. Subsequently, we explore three key trends in optical metasurfaces, including mechanically reconfigurable metasurfaces, digitally controlled metasurfaces, and conformal metasurfaces. Finally, we summarize our insights on the ongoing challenges and opportunities in this field.