Lamin proteins, predominantly located near the nuclear lamina, are known to play an important role in maintaining large-scale genome organisation. Disruptions in lamin assembly have been implicated in various diseases exhibiting altered chromatin organisation, nuclear stiffness and chromosome dynamics. Theoretical and computational modelling is essential for understanding these diverse observations through the lens of physical forces and interactions. This review focuses on modelling efforts aimed at elucidating the multifaceted role of lamins in genome organisation and how disruptions in these interactions contribute to the pathologies observed in different cell types, disease conditions and lamin mutants. We categorise the major modelling approaches used to study lamin-mediated chromatin organisation, summarise key findings within each category and highlight future directions in developing a comprehensive understanding of the role of lamins in the spatial organisation of the genome.