Engineered surfaces play a vital role in various fluid applications, serving specific functions such as self-cleaning, anti-icing, thermal management, and water energy harvesting. In nature, biological surfaces, particularly those displaying physiochemical heterogeneity, showcase remarkable fluid behaviors and functionalities, offering valuable insights for artificial designs. In this Review, we focus on exploring the fascinating fluid phenomena observed on natural biological surfaces and the manipulation of fluids on bioengineered surfaces, with a particular emphasis on droplets, liquid flows, and vapor flows. We delve into the fundamental principles governing symmetric fluid motion on homogeneous surfaces and directed fluid motion on heterogeneous surfaces. We discuss surface design strategies tailored to different fluid scenarios, outlining the strengths and limitations of engineered surfaces for specific applications. Additionally, the challenges faced by engineered surfaces in real-world fluid applications are put forward. By highlighting promising research directions, we hope to stimulate advancements in bioinspired engineering and fluid science, paving the way for future developments.