Gene co-expression networks capture biologically important patterns in gene expression data, enabling functional analyses of genes, discovery of biomarkers, and interpretation of regulatory genetic variants. Most network analyses to date have been limited to assessing correlation between total gene expression levels in a single or small sets of tissues. Here, we have reconstructed networks that capture a much more complete set of regulatory relationships, specifically including regulation of relative isoform abundance and splicing, and tissue-specific connections unique to each of a diverse set of tissues. Using the Genotype-Tissue Expression (GTEx) project v6 RNA-sequencing data across 44 tissues in 449 individuals, we evaluated shared and tissue-specific network relationships. First, we developed a framework called Transcriptome Wide Networks (TWNs) for combining total expression and relative isoform levels into a single sparse network, capturing the complex interplay between the regulation of splicing and transcription. We built TWNs for sixteen tissues, and found that hubs with isoform node neighbors in these networks were strongly enriched for splicing and RNA binding genes, demonstrating their utility in unraveling regulation of splicing in the human transcriptome, and providing a set of candidate shared and tissue-specific regulatory hub genes. Next, we used a Bayesian biclustering model that identifies network edges between genes with co-expression in a single tissue to reconstruct tissue-specific networks (TSNs) for 27 distinct GTEx tissues and for four subsets of related tissues. Using both TWNs and TSNs, we characterized gene co-expression patterns shared across tissues. Finally, we found genetic variants associated with multiple neighboring nodes in our networks, supporting the estimated network structures and identifying 33 genetic variants with distant regulatory impact on transcription and splicing. Our networks provide an improved understanding of the complex relationships between genes in the human transcriptome, including tissue-specificity of gene co-expression, regulation of splicing, and the coordinated impact of genetic variation on transcription.