Although the invention of right heart catheterisation in the 1950s enabled accurate clinical diagnosis of pulmonary arterial hypertension (PAH), it was not until 2000 when the landmark discovery of the causative role of bone morphogenetic protein receptor type II (BMPR2) mutations shed new light on the pathogenesis of PAH. Since then several genes have been discovered, which now account for around 25% of cases with the clinical diagnosis of idiopathic PAH. Despite the ongoing efforts, in the majority of patients the cause of the disease remains elusive, a phenomenon often referred to as “missing heritability”. In this review, we discuss research approaches to uncover the genetic architecture of PAH starting with forward phenotyping, which in a research setting should focus on stable intermediate phenotypes, forward and reverse genetics, and finally reverse phenotyping. We then discuss potential sources of “missing heritability” and how functional genomics and multi-omics methods are employed to tackle this problem.