Certain rotating objects with unique designs exhibit extraordinary gyroscopic effects. The Tippe top, boomerang flight, and the inversions of spinning objects during orbital flight are some of the most remarkable gyroscopic effects. One of the well-known top toys from ancient times is the Tippe top, which is more attractive than an ordinary disc-type top because of its ability to turn upside-down. Boomerang flight demonstrates the interaction of aerodynamic forces and gyroscopic effects. The inversions of spinning objects during orbital flight are also manifestations of gyroscopic effects. These remarkable gyroscopic effects are mathematically described and explained based on their physical principles. The system of inertial torques acting on spinning objects and the dependence of angular velocities of rotations about axes are used to analytically solve for their gyroscopic effects. This chapter presents mathematical models for the Tippe top turning upside-down, the inversions of spinning objects during orbital flight, and boomerang flight. Their motions are formulated based on the interrelated inertial torques acting on spinning objects and the principle of mechanical energy conservation.