It is anticipated that the decarbonisation of the entire energy system will require the introduction of large shares of variable renewable electricity generation into the power system. Long term integrated energy systems models are useful in improving our understanding of decarbonisation but they struggle to take account of short term variations in the power system associated with increased variable renewable energy penetration. This can oversimplify the ability of power systems to accommodate variable renewables and result in mistaken signals regarding the levels of flexibility required in power systems. Capturing power system impacts of variability within integrated energy system models is challenging due to temporal and technical simplifying assumptions needed to make such models computationally manageable. This paper addresses a gap in the literature by reviewing prominent methodologies that have been applied to address this challenge and the advantages & limitations of each. The methods include soft linking between integrated energy systems models and power systems models and improving the temporal and technical representation of power systems within integrated energy systems models. Each methodology covered approaches the integration of short term variations and assesses the flexibility of the system differently. The strengths, limitations, and applicability of these different methodologies are analysed. This review allows users of integrated energy systems models to select a methodology (or combination of methodologies) to suit their needs. In addition, the analysis identifies remaining gaps and shortcomings.