This dissertation investigates data reduction strategies from a signal processing perspective in centralized detection and estimation applications. First, it considers a deterministic source observed by a network of sensors and develops an analytical strategy for ranking sensor transmissions based on the magnitude of their test statistics. The benefit of the proposed strategy is that the decision to transmit or not to transmit observations to the fusion center can be made at the sensor level resulting in significant savings in transmission costs. A sensor network based on target tracking application is simulated to demonstrate the benefits of the proposed strategy over the unconstrained energy approach. Second, it considers the detection of random signals in noisy measurements and evaluates the performance of eigenvalue-based signal detectors. Due to their computational simplicity, robustness and performance, these detectors have recently received a lot of attention. When the observed random signal is correlated, several researchers claim that the performance of eigenvalue-based detectors exceeds that of the classical energy detector. However, such claims fail to consider the fact that when the signal is correlated, the optimal detector is the estimator-correlator and not the energy detector. In this dissertation, through theoretical analyses and Monte Carlo simulations, eigenvalue-based detectors are shown to be suboptimal when compared to the energy detector and the estimator-correlator.