This chapter discusses the design of unknown input observers for a class of time-delay systems with a constant time delay. Based on our newly proposed matrix decomposition technique, we can effectively obtain a reduced-order disturbance-free time-delay system, and then obtain a closed form analytical expression for the unknown input. Here, the unknown input is in the simplest form containing only one output measurement, its delayed output measurement, the first-derivative of one output measurement, and a generalized functional that contains a state-delayed term, i.e., \(z(t)=Fx(t)+F_dx(t-\tau )\) . Thus, the unknown input can be estimated if we can estimate this generalized functional. We extensively look at possible ways to realize the estimation of the generalized functional by examining various design options and scenarios. We then conclude that an effective and economical way is to estimate the generalized functional directly.