Leaf shape is a defining feature of how we recognise and classify plant species. Although there is extensive variation in leaf shape within many species, few studies have disentangled the underlying genetic architecture. We characterised the genetic architecture of leaf shape variation in Eurasian aspen (Populus tremula L.) by performing a genome wide association studies (GWAS) for physiognomy traits. To ascertain the roles of identified GWAS candidate genes within the leaf development transcriptional program, we performed gene co-expression network analyses from a developmental series, which is publicly available at http://aspleaf.plantgenie.org. We additionally used gene expression measurements across the population to analyse GWAS candidate genes in the context of a population-wide co-expression network and to identify genes that were differentially expressed between groups of individuals with contrasting leaf shapes. These data were integrated with expression GWAS (eQTL) results to define a set of candidate genes associated with leaf shape variation. Our results identified no clear adaptive link to leaf shape variation and indicate that leaf shape traits are genetically complex, likely determined by numerous small-effect variations in gene expression. Genes associated with shape variation were peripheral within the population-wide co-expression network, were not highly connected within the leaf development co-expression network and exhibited signatures of relaxed selection. As such, our results are consistent with the omnigenic model.