Genome-wide association studies (GWAS) have successfully identified a large number of genetic variants associated with complex traits, but these only explain a small proportion of the total heritability. It has been recently proposed that rare variants can create 'synthetic association' signals in GWAS, by occurring more often in association with one of the alleles of a common tag single nucleotide polymorphism. While the ultimate evaluation of this hypothesis will require the completion of large-scale sequencing studies, it is informative to place it in the broader context of what is known about the genetic architecture of complex disease. In this review, we draw from empirical and theoretical data to summarize evidence showing that synthetic associations do not underlie many reported GWAS associations.