Cytopathology is a minimally invasive, rapid, and cost-effective diagnostic modality with broad utilization in veterinary medicine. Primary care clinicians often screen common cutaneous and subcutaneous aspirates, with other samples most frequently evaluated by board certified veterinary clinical pathologists in reference laboratories. Wright-Giemsa stains are frequently utilized with the application of ancillary diagnostics such as cytochemistry, immunocytochemistry, flow cytometry, and molecular diagnostic techniques complicated by the need to develop and validate species specific reagents and protocols. The interpretation of veterinary cytology samples must be undertaken with extensive knowledge of the breadth of animal species, which includes familiarity with the frequency and biological behavior of inflammatory, infectious, and neoplastic lesions that are influenced by species, breed, and husbandry conditions. This review is the first of two parts that focus on the most common domestic companion animal species (dog, cat, and horse), taking an organ system approach to survey important lesions that may be unique to veterinary species or have interesting correlates in human medicine. The first of the two-part series covers skin and subcutaneous tissue, the musculoskeletal system, and lymphoid organs. The cytologic features and biological behavior of similar lesions are compared, and selected molecular mechanisms of disease and ancillary diagnostics are reviewed when characterized. Supporting figures illustrate a subset of lesions. While not a comprehensive catalog of veterinary cytology, the goal is to give cytopathologists working in human medicine a general impression of correlates in veterinary practice.