This thesis studies multi-phase flows within two different types of porous nature-inspired material systems: multi-layered feathers and synthetic trees. (1) How multilayered feathers enhance underwater superhydrophobicity. Inspired by ducks, here we demonstrate that air pockets can withstand up to five times more hydrostatic pressure when using stacked layers of synthetic feathers instead of a single layer. The mechanism for the multi-layered enhancement is the more tortuous pathway required for water impalement, which serves to pressurize the air pockets enclosed in the pores. We study this air compression effect using a probabilistic model, in which we quantify the tortuous pathway in stacked feather layers in terms of filled volume fraction of the pores. Our findings suggest that multi-layered coatings could enable robust underwater superhydrophobicity. (2) Oil-Water separation using synthetic trees. In the world's tallest trees, water evaporating from leaves generates enough suction to lift water over 100 m high. Transpiration can similarly be attained in synthetic trees by coupling nanoporous leaves" with conduits mimicking xylem capillaries. Here, we demonstrate that by adding filters to the free ends of the xylem conduits, the hydraulic load generated by transpiration can be used for oil-water separation. The working principle is illustrated using the pressure balance equation for the synthetic tree. / Master of Science / Nature abounds in complex systems and fascinating phenomena that have inspired us, from the way we live to the things we create. The engineering profession is no exception to being inspired by nature. In fact, engineers have created revolutinary robots inspired by animals. The work in this theis draws inspiration from the water-repellant property (superhydrophobicity) of duck feathers and the transpiration process in plants. In the first study, we created 'synthetic feathers' to study how layers of duck feathers are able to sustain superhydrophobicity under water. We discovered the 'layer-effect' that explains enhanced underwater superhydrophobicity. Surfaces covered in such multi-layered feather-like porous structures are potentially useful for reducing drag in underwater applications. In the second study, we develop a 'synthetic tree' that captures the main attributes of the transpiration mechanism in plants. We show that the 'pull' generated by transpiration can be used for oil-water separation. This macroscopic synthetic tree can be useful in cleaning oil spills.