Various parental characteristics, including psychiatric disorders and parenting behaviours, are associated with offspring mental health and related outcomes in observational studies. The application of genetically informative designs is crucial to disentangle the role of genetic and environmental factors (as well as gene-environment correlation) underlying these observations, as parents provide not only the rearing environment but also transmit 50% of their genes to their offspring. This article first provides an overview of behavioural genetics, matched-pair, and molecular genetics designs that can be applied to investigate parent-offspring associations, whilst modelling or accounting for genetic effects. We then present a systematic literature review of genetically informative studies investigating associations between parental characteristics and offspring mental health and related outcomes, published since 2014. The reviewed studies provide reliable evidence of genetic transmission of depression, criminal behaviour, educational attainment, and substance use. These results highlight that studies that do not use genetically informative designs are likely to misinterpret the mechanisms underlying these parent-offspring associations. After accounting for genetic effects, several parental characteristics, including parental psychiatric traits and parenting behaviours, were associated with offspring internalising problems, externalising problems, educational attainment, substance use, and personality through environmental pathways. Overall, genetically informative designs to study intergenerational transmission prove valuable for the understanding of individual differences in offspring mental health and related outcomes, and mechanisms of transmission within families.