The cell cycle is the fundamental process that underpins the generation of two daughter cells from a mother cell. Single-cell studies have revealed that genetically identical cells display differences in the time they spend progressing through the cell cycle. Deciphering how cell cycle length heterogeneity arises will have important implications for understanding aspects of cancer development and tumour relapse. Evidence from time-lapse microscopy suggests that cell cycle variation can be linked to transcription factor dynamics and how they interface with the cell cycle. This thesis sought to describe the expression dynamics and ultimately function of the transcription factor HES1 during the cell cycle in the MCF7 breast cancer cell line. Single-cell measurement of HES1 transcription was performed using single-molecule fluorescence in-situ hybridisation (smFISH). A recently published HES1 inhibitor (JI051) was characterised by examining its effect on cell cycle progression, HES1 protein dynamics and HES1 target binding. HES1 expression displayed substantial cell-to-cell heterogeneity in MCF7 cells. An increase in the number of HES1 transcription start sites and mRNA transcripts per cell was observed in cells with a higher DNA content, indicating that HES1 transcription is dynamic and potentially upregulated during cell cycle progression. The dominant effect of JI051 on the cell cycle was found to be a prolonged mitotic arrest without an impairment of cell cycle progression prior to mitosis. Although, nuclear expression of HES1 was decreased in a proportion of JI051-treated cells, cells arrested in mitosis regardless of any change in HES1 expression. Sustained CCNB1 expression was identified as a notable gene expression change occurring in JI051-treated cells. Whether CCNB1 or transcriptional activators of CCNB1 were de-repressed due to JI051 treatment was investigated by ChIP-sequencing. No mechanistic link was identified between sustained CCNB1 expression and HES1. Nonetheless, several novel HES1 targets were identified that will serve as useful information for the study of HES1 in a breast cancer context. Moreover, HES1 binding to its own promoter (a regulatory requirement for HES1 dynamics) was verified and found to be differentially enriched at distinct timepoints in G1, indicating that HES1 expression may be modulated during the cell cycle by negative feedback in MCF7 cells.