Alzheimer's disease (AD), the most common form of dementia worldwide, is a mixed proteinopathy (β-amyloid, tau and other proteins). Classically defined as a clinicopathological entity, AD is a heterogeneous, multifactorial disorder with various pathobiological subtypes showing different forms of cognitive presentation, currently referred to as the Alzheimer spectrum or continuum. Its morphological hallmarks are extracellular β-amyloid (amyloid plaques) and intraneuronal tau aggregates forming neurofibrillary tangles and neurites, vascular amyloid deposits (cerebral amyloid angiopathy), synapse and neuronal loss as well as neuroinflammation and reactive astrogliosis, leading to cerebral atrophy and progressive mental/cognitive impairment (dementia). In addition to "classical" AD, several subtypes with characteristic regional patterns of tau pathology have been segregated that are characterized by distinct clinical features, differences in age, sex distribution, disease duration, cognitive status, APOE genotype, and biomarker levels. In addition to four major subtypes based on the distribution of tau pathology and brain atrophy (typical, limbic predominant, hippocampal sparing, and minimal atrophy), several other clinical variants (non-amnestic, corticobasal, behavioral/dysexecutive, posterior cortical variants, etc.) have been identified. These heterogeneous AD variants are characterized by different patterns of key neuronal network destructions, in particular the default-mode network that is responsible for cognitive decline. Other frequent age-related co-pathologies, e.g., cerebrovascular lesions, Lewy and TDP-43 pathologies, hippocampal sclerosis, or argyrophilic grain disease, essentially influence the clinical picture and course of AD, and can challenge our understanding of this disorder including the threshold and causal relevance of each individual pathology. Unravelling the clinico-morphological heterogeneity among the AD spectrum entities is important for better elucidation of the pathogenic mechanisms affecting the aging brain that may enable a broader diagnostic coverage of AD as a basis for implementing precision medicine approaches and for developing preventive and ultimately disease-modifying therapies for this devastating disorder.