The determination of transcriptional regulatory networks is key to the understanding of biological systems. However, the experimental determination of transcriptional regulatory networks in the laboratory remains difficult and time-consuming, while current computational methods to infer these networks (typically from gene-expression data) achieve only modest accuracy. The latter can be attributed in part to the limitations of a single-organism approach. Computational biology has long used comparative and, more generally, evolutionary approaches to extend the reach and accuracy of its analyses. We therefore use an evolutionary approach to the inference of regulatory networks, which enables us to study evolutionary models for these networks as well as to improve the accuracy of inferred networks. Since the regulatory networks evolve along with the genomes, we consider that the regulatory networks for a family of organisms are related to each other through the same phylogenetic tree. These relationships contain information that can be used to improve the accuracy of inferred networks. Advances in the study of evolution of regulatory networks provide evidence to establish evolutionary models for regulatory networks, which is an important component of our evolutionary approach. We use two network evolutionary models, a basic model that considers only the gains and losses of regulatory connections during evolution, and an extended model that also takes into account the duplications and losses of genes. With the network evolutionary models, we design refinement algorithms to make use of the phylogenetic relationships to refine noisy regulatory networks for a family of organisms. These refinement algorithms include: RefineFast and RefineML, which are two-step iterative algorithms, and ProPhyC and ProPhyCC, which are based on a probabilistic phylogenetic model. For each algorithm we first design it with the basic network evolutionary model and then generalize it to the extended evolutionary model. All these algorithms are computationally efficient and are supported by extensive experimental results showing that they yield substantial improvement in the quality of the input noisy networks. In particular, ProPhyC and ProPhyCC further improve the performance of RefineFast and RefineML. Besides the four refinement algorithms mentioned above, we also design an algorithm based on transfer learning theory called tree transfer learning (TTL). TTL differs from the previous four refinement algorithms in the sense that it takes the gene-expression data for the family of organisms as input, instead of their inferred noisy networks. TTL then learns the network structures for all the organisms at once, meanwhile taking advantage of the phylogenetic relationships. Although this approach outperforms an inference algorithm used alone, it does not perform better than ProPhyC, which indicates that the ProPhyC framework makes good use of the phylogenetic information.