This chapter deals with the fault estimation and detection problems for linear discrete time-varying systems over a finite horizon. Firstly, the \(H_\infty \) fault estimation issue is considered for a kind of linear discrete time-varying systems with both instantaneous and delayed measurements. By utilizing the reorganized innovation approach, the measurements are reorganized into a tractable form, based on which we introduce an associated stochastic system in a Krein space. With the help of innovation analysis and projection theory in the Krein space, a necessary and sufficient condition for the existence of the finite-horizon \(H_{\infty }\) fault estimator is obtained and then a fault estimator is designed in terms of the solution to certain Riccati difference equations. Subsequently, by using similar analysis techniques, the \(H_{\infty }\) fault estimation problem is also studied for a general class of uncertain discrete time-varying systems with known inputs, and a set of parallel results is derived. Moreover, considering the fact that the FD problem can often be converted into an auxiliary \(H_\infty \) fault estimation problem, the other research of this chapter is to investigate the FD problem, into which a residual generation, evaluation, and threshold are integrated, for linear discrete time-varying systems. The purpose of this problem addressed is to propose a FD scheme to realize the residual generation in the \(H_{\infty }\) fault estimation framework and introduce the FARI and FDRI in the norm-based framework which is integrated into the decision-making process. Finally, some numerical examples are exploited to illustrate the main results of this chapter.