In the last 40 years there have been many strides taken towards better and more selective cancer treatment using nanoparticles. Nanoparticles can have inherent passive accumulation in tumour cells, known as the enhanced permeability and retention effect (EPR) which makes them a strong therapy candidate; however this effect is not as well defined or effective as once thought. There is a large variance of efficacy between different patients due to the heterogeneity of tumours, therefore a more targeted nanoparticle systems needs to be designed to increase selectivity and efficacy. This thesis describes the design, synthesis, and characterisation of 20 novel ellipsoidal polymersomes decorated with peptide ligands for selective targeting of medulloblastoma, a childhood brain cancer. These ligands were FSRPAFL 1 a medulloblastoma cell targeting peptide and T7 26 a transferrin targeting peptide designed to aid in crossing the blood brain barrier (BBB). A new synthetic method was designed to attach the peptide ligands post self-assembly, so the peptides were attached to the hydrophilic corona rather than the hydrophobic membrane of the polymersomes. Analysis of these polymersomes showed more ligand available for binding but this did not translate to increased cell association due to an over saturation of ligand. The ratio and density of the targeting peptide 1 and BBB peptide 26 was altered on the surface of the polymersomes and it was found that the polymersomes with 100% T7 ligand showed rapid and high cell association with two different subtypes of SHH medulloblastoma (DAOY and UW228) as well as high association with brain endothelial cells that make up the BBB (HBEC-5i) making it a promising candidate as a drug delivery system for SSH medulloblastoma. Finally, linearly conjugated dual peptides made up of both targeting peptide 1 and T7 peptide 26 sequence, were synthesised and attached to the polymersome hydrophilic corona and analysed against the non-conjugated dual-functionalised peptide polymersomes. There was no significant difference between the two ligand conjugation method analysed but further research should be conducted to confirm this. The work described in this Thesis has shed light on the multitude of nuances that make up the composition of mono and dual functionalised peptide nanoparticle systems and how these can influence biological function. Future work will allow for a better understanding of fundamental questions about targeted nanoparticles therapies and how ligand characteristics directly impact biological function, selectivity and efficacy.