Hepatitis E virus (HEV) is a small quasi-enveloped, (+)-sense, single-stranded RNA virus belonging to the family. There are at least 20 million HEV infections annually and 60,000 HEV-related deaths worldwide. HEV can cause up to 30% mortality in pregnant women and progress to liver cirrhosis in immunocompromised individuals and is, therefore, a greatly underestimated public health concern. Although a prophylactic vaccine for HEV has been developed, it is only licensed in China, and there is currently no effective, non-teratogenic treatment. HEV encodes three open reading frames (ORFs). ORF1 is the largest viral gene product, encoding the replicative machinery of the virus including a methyltransferase, RNA helicase, and an RNA-dependent RNA polymerase. ORF1 additionally contains a number of poorly understood domains including a hypervariable region, a putative protease, and the so-called 'X' and 'Y' domains. ORF2 is the viral capsid essential for formation of infectious particles and ORF3 is a small protein essential for viral release. In this review, we focus on the domains encoded by ORF1, which collectively mediate the virus' asymmetric genome replication strategy. We summarize what is known, unknown, and hotly debated regarding the coding and non-coding regions of HEV ORF1, and present a model of how HEV replicates its genome.