Asthma is a chronic inflammatory lung disease, characterised by hyperresponsiveness (excessive contraction of smooth muscle cells lining the airways) and remodelling (structural changes to the airway). The mechanisms underlying the disease, and how these characteristics are related, are poorly understood. In this talk I will first focus on the role of breathing and deep inspirations (DI) in modulating airway hyper-responsiveness. I will present predictions from a validated biomechanical model of the intact airway, accounting for strain-stiffening due to collagen recruitment (a large component of the extracellular matrix), and dynamic actomyosin-driven force generation by smooth muscle cells, and how the predictions lead to testable hypotheses. I will then describe a preliminary inflammation-driven morphoelastic model of growth in which the evolving effective mechanical properties of the tissue comprising smooth muscle cells and collagen affect remodelling. I will finish with a discussion of how hyper-responsiveness and remodelling could therefore be related in the asthmatic airway.