Breast cancer is the most common cancer in the UK and in women globally. Imaging methods like mammography, ultrasound (US) and magnetic resonance imaging (MRI) play an important role in the diagnosis and management of breast cancer; they are generally utilised to provide anatomical or structural description of tumours in the clinical setting. It is widely accepted that the tumour microenvironment influences the phenotype, progression and treatment of breast cancer. This gave the impetus to move beyond tumour visualization in images to radiomics in order to provide additional disease characterisation and early biomarkers of tumour response. Due to their ability to assess physiological processes in vivo, positron emission tomography (PET) and MRI can provide non-invasive characterisation of the tumour microenvironment, including perfusion, vascular permeability, cellularity and hypoxia, which is associated with poor clinical outcome and metastasis. Clinical imaging studies in breast tumours have hitherto assessed tumour physiological parameters separately, with only few directly comparing data from these modalities. To this end, hybrid PET-MRI represents an attractive option as it can allow examination of functional processes and features of tumours simultaneously, while also conferring methodological advantages to the way imaging information is combined. The main aim of this thesis is to provide a better understanding of breast cancer pathophysiology using simultaneous PET and multi-parametric MRI. In particular, this work aims to explore relationships between imaging biomarkers of tumour vascularity measured by dynamic contrast-enhanced (DCE) MRI, cellularity using diffusion-weighted imaging (DWI) and hypoxic status using 18F-fluoromisonidazole (18F-FMISO) PET. Correlations between functional PET-MRI parameters and immunohistochemical (IHC) biomarkers of hypoxia and vascularity as well as MRI morphological tumour descriptors are also presented. The thesis concludes with an investigation of the utility of MRI markers of perfusion and surrogate markers of hypoxia to quantitatively monitor and predict pathological response in patients undergoing neoadjuvant chemotherapy (NACT) and provides projections for future work.