DNA methylation is regarded as a stable epigenetic mark given its faithful maintenance across successive cell divisions. Methylation occurs at most CpG sites in mammalian genomes and is generally associated with transcriptional repression. An accepted evolutionary role for DNA methylation is to prevent the mobility of transposable elements (TEs). This thesis investigates the stability of DNA methylation in two separate contexts, particularly relating to intermediate levels of methylation. First, I characterise the properties of variably methylated TEs (VM-TEs) between individual mice. Second, I assess the fidelity of DNA methylation inheritance across cellular generations at VM-TEs, and more widely at the genome-scale, to ascertain the heritability, mechanism, and function of intermediate methylation states. My findings show that variable methylation extends beyond the boundaries of the TEs, and that all VM-TEs are enriched for binding of the transcription factor CTCF, which is inversely correlated with DNA methylation. I propose that molecular antagonism between CTCF and DNA methylation machinery influences the formation of variably methylated states in the early embryo. Within an individual mouse, VM-TEs are intermediately methylated between 10% and 90%, representing the cell population average of methylation states. The prevailing hypothesis supports the notion that methylation is established de novo by DNA methyltransferases DNMT3A/3B and then faithfully maintained by DNMT1. Hence, intermediate methylation levels likely represent stochastic de novo establishment (DNMT3A/3B) and clonal maintenance (DNMT1) within the cell population. To test this, I subcloned single cells from both mouse embryonic fibroblasts (MEFs) and embryonic stem cells (mESCs), growing them into multiple subclonal populations to assess methylation fidelity through cell divisions. This allowed me to address the degree to which a particular locus acquires intermediate methylation in the clonal population, as well as the properties and mechanism of that state. If methylation is indeed propagated faithfully, one would expect that the single-cell derived populations always exhibit one of the three symmetric methylation states: 0%, 50% or 100%. At VM-TEs, we find that the subcloned cell lines attain intermediate methylation levels that reflect the level of the parent population, which implies that the original single-cell methylation state is not faithfully maintained at these loci. Expanding the analysis genome-wide, I use a target capture bisulphite sequencing method to evaluate methylation fidelity in the subclonal cell lines more globally. I find that CpGs exhibiting intermediate methylation at the cell population level, are generally unfaithfully inherited between cell divisions and attain methylation independently of neighbouring CpGs. While faithful hypo- and hypermethylation associate with transcriptional activity, unfaithful intermediate methylation associates with transcriptionally inactive genes or intergenic regions of the genome. Finally, in DNMT3A/3B mutants, methylation is not depleted consistently at any CpG, regardless of its methylation state in the control. Therefore, DNMT1 has two functions: 1) canonical maintenance of faithful methylation and 2) as shown here, it is responsible for the acquisition of intermediate methylation states that are unfaithfully inherited between cell divisions.