Wireless sensor networks (WSNs) are gaining attention in recent years. Considering the potential low cost of a single sensor-processor unit in the near future, it is envisioned that there will be large-scale deployments of sensor networks for various applications: environmental, medical, inventory control, energy management, structural health monitoring, etc. A WSN comprises of a large number of nodes that individually have limited energy and computational power; however, by cooperating with each other, they can jointly perform tasks that are difficult to handle by traditional centralized sensing systems;In this dissertation, spatial and spatio-temporal signal processing methods are developed for WSNs: (1) Distributed estimation and detection using hidden Markov random fields: We derive ICM algorithms for distributed estimation of the hidden random field from the noisy measurements and consider both parametric and nonparametric measurement-error models. (2) Parametric signal estimation in the presence of node localization errors: We propose a Bayesian framework that accounts for the inherent uncertainties in the node locations (caused by the node localization errors) and develop an estimation method that is robust to these uncertainties. (3) Event-region estimation under the Poisson regime: We propose a parametric model for the location and shape of the event region and develop a Bayesian method for event-region estimation in large-scale sensor networks. (4) Sequential mean-field estimation and detection in spatially correlated Gaussian fields: We propose distributed methods for estimating and detecting the mean of a correlated Gaussian random field observed by a sensor network;We consider estimation and detection of both localized and global phenomena and practically important nonparametric scenarios where the distribution of the measurements is unknown.