Skyrmions are topologically nontrivial, magnetic quasiparticles that are characterized by a topological charge. The field of magnetic skyrmions has been actively investigated across a wide range of topics during the last two decades. We mainly reviewed and discussed magnetic skyrmions, and quasiparticles: reviews on principles and applications. We concentrated on theoretical discoveries and advances in magnetic skyrmions, topological effects, the skyrmion Hall effect, and the dynamics of skyrmions. The skyrmion Hall effect causes a transverse deflection of skyrmions when they are driven by currents, whereas the first additional contribution to the Hall effect of electrons in the presence of a topologically non-trivial spin texture may become beneficial for detecting skyrmions. This means that when a current is applied along the racetrack, skyrmions are pushed toward the edge, causing pinning or possibly the loss of data. This is one of the reasons why there is currently no prototype for a spintronic device based on skyrmions. The anti-ferromagnetic and ferrimagnetic skyrmions were then discussed in relation to spintronics. Finally, we reviewed several potential applications based on magnetic skyrmions, including skyrmion race track memory, a skyrmion logical device, a skyrmion magnonic crystal, and skyrmion-based radio frequency devices.