The Medical Services Advisory Committee (MSAC) is an independent non-statutory committee established by the Australian government to provide recommendations on public reimbursement of technologies and services, other than pharmaceuticals. MSAC has established approaches for undertaking health technology assessment (HTA) of investigative services and codependent technologies. In 2016, MSAC published its clinical utility card (CUC) Proforma, an additional tool to guide assessments of genetic testing for heritable conditions. We undertook a review and narrative synthesis of information extracted from all MSAC assessments of genetic testing for heritable conditions completed since 2016, regardless of the HTA approach taken. Ten assessments met our inclusion criteria, covering a range of testing methods (from gene panels to whole-exome sequencing) and purposes (including molecular diagnosis, genetic risk assessment, identification of congenital anomaly syndromes, and carrier screening). This analysis identified a range of methodological and policy challenges such as how to incorporate patient and societal preferences for the health and non-health outcomes of genomic testing, how best to capture the concept of co-production of utility, and how to engage clinicians as referrers for genomics tests whilst at the same time ensuring equity of access to a geographically dispersed population. A further challenge related to how qualitative assessments of patient and community needs influenced the evidence thresholds against which decisions were made. These concepts should be considered for incorporation within the value assessment frameworks used by HTA agencies around the world.