Wireless sensor networks (WSN) are an emerging technology with a wide range of applications including environment monitoring, security and surveillance, health care, smart homes, etc. Subject to severe resource constraints in wireless sensor networks, in this research, we address the distributed estimation of unknown parameters by studying the correlation among resource, distortion, and lifetime, which are three major concerns for WSN applications. The objective of the proposed research is to design efficient distributed estimation algorithms for resource-constrained wireless sensor networks, where the major challenge is the integrated design of local signal processing operations and strategies for inter-sensor communication and networking so as to achieve a desirable tradeoff among resource efficiency (bandwidth and energy), system performance (estimation distortion and network lifetime), and implementation simplicity. More specifically, we address the efficient distributed estimation from the following perspectives: (i) rate-distortion perspective, where the objective is to study the rate-distortion bound for the distributed estimation and to design practical and distributed algorithms suitable for wireless sensor networks to approach the performance bound by optimally allocating the bit rate for each sensor, (ii) energy-distortion perspective, where the objective is to study the energy-distortion bound for the distributed estimation and to design practical and distributed algorithms suitable for wireless sensor networks to approach the performance bound by optimally allocating the bit rate and transmission energy for each sensor, and (iii) lifetime-distortion perspective, where the objective is to maximize the network lifetime while meeting estimation distortion requirements by jointly optimizing the source coding, source throughput and multi-hop routing. Also, energy-efficient cluster-based distributed estimation is studied, where the objective is to minimize the overall energy cost by appropriately dividing the sensor field into multiple clusters with data aggregation at cluster heads.