Bolt connection structure is a common form of connecting large and complex equipment. Its object contact surfaces under normal and tangential loads will appear in the form of slip and adhesion, which affects the service life of mechanical equipment. Bolted connection structures cause changes in stiffness and damping, which have great impacts on the dynamic characteristics. Experimental studies and numerical simulations have difficulty predicting the overall performance of bolts in a timely manner, hence cannot ensure the reliability and safety of complex equipment. In order to improve the overall performance of complex equipment, it is necessary to study the contact theory model of bolt connection structures. Based on the relationship between friction force and velocity in the classical friction model, the mathematical expressions of restoring force and tangential displacement in the kinetic theory model are deduced to predict the stiffness degradation of the bolted structure and to characterise the kinetic properties and laws of the bolted structure. From the perspective of theoretical calculation, it makes up for the situation in which it is difficult to measure the performance of bolts due to the existence of spanning scale and provides theoretical support for the reliability of connecting complex equipment. This paper summarises and analyses the contact theory model of bolt connection structures, ranging from macroscopic to microscopic; describes the static friction model, kinetic friction model, statistical summation contact model, fractal contact model; and analyses the influencing factors of the microscopic contact mechanism. The advantages and disadvantages of the kinetic theoretical models are described, the manifestation of friction and the relationship between tangential force–displacement are discussed, and the key research directions of the kinetic theoretical models of bolted structures in the future are elucidated.