In this thesis, I examine both applied and theoretical issues in network source coding. The applied results focus on the construction of locally rate-distortion-optimal vector quantizers for networks. I extend an existing vector quantizer design algorithm for arbitrary network topologies  to allow for the use of side information at the decoder and for the presence of channel errors. I show how to implement the algorithm and use it to design codes for several different systems. The implementation treats both fixed-rate and variable-rate quantizer design and includes a discussion of convergence and complexity. Experimental results for several different systems demonstrate in practice some of the potential performance benefits (in terms of rate, distortion, and functionality) of incorporating a network's topology into the design of its data compression system. The theoretical work covers several topics. Firstly, for a system with some side information known at both the encoder and the decoder, and some known only at the decoder, I derive the rate-distortion function and evaluate it for binary symmetric and Gaussian sources. I then apply the results for binary sources in evaluating the binary symmetric rate-distortion function for a system where the presence of side information at the decoder is unreliable. Previously, only upper and lower bounds were known for that problem. Secondly, I address with an example the question of whether feedback from a decoder to an encoder ever enlarges the achievable rate region for lossless network source coding of memoryless sources. Thirdly, I show how cutset methods can yield quick and simple rate-distortion converses for any source coding network. Finally, I present rate-distortion results for two different broadcast source coding systems.