Telomeres cap the ends of eukaryotic chromosomes, masking the end from DNA repair processes and preventing end-to-end fusions. Telomeres shorten progressively with each cell division, eventually becoming dysfunctional and producing a signal that results in cellular senescence. Telomere shortening can be counteracted by telomerase, a ribonucleoprotein complex with reverse transcriptase activity that catalyses the addition of nucleotide repeats to the end of the telomere. During normal human development, telomerase expression is restricted to the germ cells, some adult stem cells and the early embryo. Correspondingly, telomerase is highly expressed in human embryonic stem cells (hESCs), which are derived from the inner cell mass of the blastocyst and are able to self-renew indefinitely and differentiate into cells of all three germ layers. hESCs provide a useful model for studying telomerase biology during human development therefore I aimed to study the regulation of telomerase in hESCs and their neural progeny. The research in this thesis revealed that whilst telomerase was downregulated during hESC neural differentiation and telomeres of the derived neural progenitor/stem cells (NPSCs) shortened extensively, telomerase became reactivated in the NPSCs following extended culture, leading to telomere elongation. Furthermore, this reactivation occurred in the absence of cellular transformation. Telomerase reverse transcriptase (hTERT) expression in hESCs and their derived NPSCs was found to be regulated by dynamic DNA methylation of the hTERT promoter and this methylation regulated hTERT transcription by blocking the binding of the transcriptional activator Sp1. The impact of telomerase expression on hESC self-renewal and differentiation was studied using hESCs that constitutively expressed hTERT. This showed that while hTERT expression only resulted in a minor delay in hESC differentiation, NPSCs derived from these hESCs had a compromised differentiation potential, suggesting that overexpression of hTERT has a more profound effect in somatic stem cells than it does in embryonic stem cells.