Interactions of suspended particles with interfaces are important in many natural and engineered systems including examples in lubricated bearings, blood flow and microfluidics. In the first part of my talk, I will discuss a microfluidic application that uses ultrasound-driven bubbles to either sort or trap microparticles by size. I will present a predictive model that shows that particle sorting and trapping result from an interplay between the particle's inertia and hydrodynamic interactions with the oscillating bubble interface. I will go on to discuss limiting cases of strong and weak interactions which recovers results from geometry and acoustics, respectively. The second part of the talk addresses situations where interface deformation, mediated by hydrodynamic interactions, is a direct consequence – and a subsequent cause – of particle motion. I will present experiments demonstrating that rigid particles translating near a flexible elastic membrane are repelled by it due to hydrodynamic interactions. A model of these interactions involving membrane tension and bending will then be discussed, leading to a general framework for particle hydrodynamics near interfaces and soft substrates. The results suggest that similar interactions may play a role in blood flow and cellular processes at the micron scale.