This chapter considers the problem of estimating an unknown input in the presence of multiple unknown inputs in the system. The designed unknown input observer asymptotically estimates a targeted unknown input, while it is insensitive to the rest of the unknown inputs. We provide a detailed analysis of two design approaches and discuss their advantages and drawbacks. Together, they offer the designer a viable tool for designing an unknown input observer with the least number of output differentiators and a reduced-order functional observer. The results derived in this chapter are then used to design distributed unknown input observers for interconnected dynamical systems. Here, at each local subsystem, an unknown input observer is designed to estimate the local unknown inputs, while the designed observer is insensitive to the external unknown inputs that go into the other subsystems.