Livestock production is faced with many challenges such as climate change, food security, globalization, sustainability, competition for natural resources, animal health and welfare. To address this intricate set of issues, the multiple dimensions of livestock farming systems have to be put in perspective. As a changing paradigm, the scale of approach is enlarged from a local focus to a holistic view on agro-ecosystem functioning and criticality at the territory level, which is intuitively posited as a complex problem. The term complex pertains to the difficulty in predicting properties from the segregation in sub-properties. Complexity thus emerges from the dependencies between the sub-parts of the whole. At first sight, the complexity of livestock farming systems emerges from the multiple relations in time and space between its main components (farmers, farmlands, animals, products, crops, resources, facilities, wastes, etc) and with components of other systems of its environment (landscapes, consumers, stakeholders, institutions, fauna/flora, pathogens, markets, water, soil, air, etc). Classically, the functioning of livestock farming systems is depicted by way of the cross-linkage of an anthropical (husbandry activities) and a biological (physiological processes) subsystem. An essential feature of the latter one is its organization through hierarchical levels (individuals, batches, herds, breeds, species), which constitutes a structural step in the organization of the whole order of the system and a functional step in the emergence of a global property of the system. Any attempt to disentangle the complexity of livestock farming systems requires considering interactions between components of the system at a given level (horizontal complexity) and integration of the system through higher levels (vertical complexity). The present communication proposes two alternative and complementary views to highlight the horizontal and vertical complexities of livestock farming systems.