Transcriptional regulation and posttranscriptional processing underlie many cellular and organismal phenotypes. We used RNA sequence data generated by Genotype-Tissue Expression (GTEx) project to investigate the patterns of transcriptome variation across individuals and tissues. Tissues exhibit characteristic transcriptional signatures that show stability in postmortem samples. These signatures are dominated by a relatively small number of genes - which is most clearly seen in blood - though few are exclusive to a particular tissue and vary more across tissues than individuals. Genes exhibiting high interindividual expression variation include disease candidates associated with sex, ethnicity, and age. Primary transcription is the major driver of cellular specificity, with splicing playing mostly a complementary role; except for the brain, which exhibits a more divergent splicing program. Variation in splicing, despite its stochasticity, may play in contrast a comparatively greater role in defining individual phenotypes.