All living organisms contain genes. Turning these genes on and off at the appropriate times controls much of an organism’s development and its responses to environmental conditions. In recent years, chromatin has emerged as an important player in orchestrating gene regulation. This thesis focuses on the role of chromatin in the maintenance of gene expression states and their inheritance through cell division. FLOWERING LOCUS C (FLC) in the plant Arabidopsis thaliana is repressed by the prolonged cold of winter, and repression is maintained in subsequent warm conditions. The molecular complexes involved in modulating FLC chromatin are vital for FLC regulation and are conserved among plants and animals, making FLC a paradigmatic system for understanding of the role of chromatin in gene regulation. After cold, FLC chromatin adopts a distinct configuration. In this study, experiments are used to show that this local chromatin ‘state’ instructs its own inheritance through cell division in growing plants. Thus, memory of winter cold is stored in the chromatin of the FLC gene. Mathematical models developed in this work focus on understanding how chromatin states are maintained and also re-established after DNA replication. Minimal models are used to investigate if a particular set of interactions between chromatin and chromatin-modifiers can give rise to the qualitative behaviours, and quantitative results that are observed experimentally. Models developed here make predictions for the FLC system, and more generally show how cis and trans determinants of gene expression can be integrated by chromatin. The role of transcription in determining chromatin states is also examined experimentally by studying the chromatin-associated protein LHP1. LHP1 is required for FLC repression and binds to modified histones associated with repressed FLC chromatin. In this work, it is shown that LHP1 also binds RNA and that this is important for its in vivo function.