This monograph presents an introductory overview of smart structures, their concepts, their active involvement in the vibration control, their applications and the extensive research work done on it so far.The modelling of flexible beams using two types of beam theories, viz., the Euler-Bernoulli theory and the Timoshenko beam theory is presented, including a new concept of finite element modeling of the flexible structures using Timoshenko beam theory with the inclusion of the shear both in the piezo-patches as well as in the host structure. It presents the design of the periodic output feedback control system for smart structure systems, the design of the FOS controllers for active vibration control and the design of Discrete Sliding Mode controllers using multirate output feedback technique.This monograph is based on the authors work on the multirate output sampling techniques (FOS and POF) and the multirate output feedback based discrete-time sliding mode control of flexible beams with simulations performed in Matlab. The hardware implementation of some of the developed control algorithms is depicted using DSpace and Real Time Workshop.