The Industrial Revolution forced scientists and practitioners to devise new analytical methods to design machines and devices for solutions to technical problems. New industrial time is manifested by an intensification of the work of machinery in which rotating objects have shown the action of intricate inertial forces and motions that are called gyroscopic effects. Later, this property will be used in many devices for aviation, space, and other industries. Contemporary research on the dynamics of rotating objects solved many gyroscope problems in engineering based on the principles and rules of classical mechanics. This chapter contains two sections. The first is a brief history of gyroscopic effects and applications in the aerospace and ship industries. The short classifications of the gyroscopes, their characteristics, technical data, and area of applications. The second section presents information about the fundamental laws, physical units and dimensions, and principles of engineering mechanics. This information is used for mathematical modeling of acting forces on rotating objects, and their motions that are used for describing the physics of gyroscopic effects. The knowledge of the basis of classical mechanics enables solving the wide engineering problems of industries related to gyroscopic devices and their practical applications.