To understand the regulation of tissue-specific gene expression, the GTEx Consortium generated RNA-seq expression data for more than thirty distinct human tissues. This data provides an opportunity for deriving shared and tissue specific gene regulatory networks on the basis of co-expression between genes. However, a small number of samples are available for a majority of the tissues, and therefore statistical inference of networks in this setting is highly underpowered. To address this problem, we infer tissue-specific gene co-expression networks for 35 tissues in the GTEx dataset using a novel algorithm, GNAT, that uses a hierarchy of tissues to share data between related tissues. We show that this transfer learning approach increases the accuracy with which networks are learned. Analysis of these networks reveals that tissue-specific transcription factors are hubs that preferentially connect to genes with tissue specific functions. Additionally, we observe that genes with tissue-specific functions lie at the peripheries of our networks. We identify numerous modules enriched for Gene Ontology functions, and show that modules conserved across tissues are especially likely to have functions common to all tissues, while modules that are upregulated in a particular tissue are often instrumental to tissue-specific function. Finally, we provide a web tool, available at mostafavilab.stat.ubc.ca/GNAT, which allows exploration of gene function and regulation in a tissue-specific manner.