Aphasia can arise due to stroke (post-stroke aphasia, PSA) or neurodegeneration (primary progressive aphasia, PPA). Two clinical and theoretical issues of relevance to PSA and PPA are addressed in this thesis. First, there have been few detailed direct comparisons across the full phenotypic ranges of PSA and PPA. Second, graded differences between aphasic subtypes and within-subtype heterogeneity suggest that phenotype differences observed across patients might reflect graded variations across multidimensional aphasic spectra rather than mutually exclusive diagnostic categories. Thus, the aim of this thesis was to compare directly the full ranges of PSA and PPA using a graded multidimensional framework to map out graded intragroup and intergroup differences. Chapter 2 uncovered graded variation in PSA and PPA along phonological, semantic, and fluency-related dimensions. Plotting all cases in the transdiagnostic shared multidimensional space revealed that 'fluent' PSA were often less fluent than 'non-fluent' PPA. Classification analysis showed that semantic dementia occupied a unique region of this multidimensional space due to the selectivity of the semantic deficit. Chapter 2 highlighted the importance of a shared test battery for this transdiagnostic approach. The Mini-Linguistic State Examination (MLSE) is a novel clinical assessment tool which is in development to address the lack of a standardised linguistic assessment tool valid for aphasia across aetiologies. Chapter 3 conducted the first formal validation of the MLSE and compared it to established aphasia tests, finding that the MLSE is highly sensitive to the presence of language impairments in PSA. Chapter 4 compared linguistic impairments across PSA and PPA on the MLSE, extending the multidimensional framework from Chapter 2 by extracting brain-behaviour relationships that underly variance in aphasia across aetiologies. Language impairments across PSA and PPA varied along three key dimensions: phonology, semantics and syntax, which were related to unique neural correlates in: left hemisphere superior and posterior temporal lobe, bilateral anterior temporal lobes, and left hemisphere subcortical regions and periventricular white matter, respectively. Chapter 5 extended the multidimensional framework to typical amnestic Alzheimer's disease (AD) and atypical visual variant AD. These groups varied gradedly along a spectrum of visual processing impairments; typical AD with mild visual impairments and mild visual variant AD overlapped in the middle of this spectrum. Overall, the transdiagnostic, multidimensional approach applied in this thesis highlights that considering patient variance along continuous dimensions instead of categorical systems has benefits for comparing directly the full phenotypic space of different disorders and relating principal behavioural dimensions to unique neural correlates of structural brain abnormalities.