Microelectronic technologies have been developing rapidly in the past half-century following the famous Moore's Law. However, this tendency is beginning to break down due to the thermal effects induced by the leakage current and data traffic. Spintronics sheds light on eliminating this bottleneck by using the spin degree of electron, which attracts great attention from both the academia and industry. The magnetic skyrmion is a particle-like spin texture with topological protection, envisioned as an energy efficient spintronic information carrier due to its nanoscale size, ultra-low driven energy, and high thermal stability. Recent research progress shows that the nucleation, transportation, and detection of skyrmion in room temperature, which affirm its potential application in electronics, lead to a new research field called skyrmionics. In this review article, we first introduce the fundamental concepts and recent progress of magnetic skyrmions, from both the theoretical and experimental point of view. Different types of magnetic skyrmions have different properties due to their physical dynamics. We only focus on the skyrmions stabilized by Dzyaloshinskii-Moriya interaction (DMI) in the ultra-thin film structures as their small size, high mobility and room temperature stability can provide the perspectives for electronic devices. The skyrmions have already been extensively investigated from both the theoretical and experimental aspects in recent years. Micromagnetic simulation is the main approach to theoretically studying the dynamics of skyrmions and their applications. Most of the innovative skyrmionic devices have first been demonstrated by this method. Experimentally, skyrmions can be measured by various methods, such as the neutron scattering, Lorentz transmission electron microscopy, scanning X-ray transmission microscopy, polar magneto-optical Kerr effect microscope, etc. In the third part of this paper, we present four basic functions of skyrmionic devices ranging from nucleation, motion, detection, to manipulation. The nucleation of skyrmions, corresponding to the information writing in skyrmionic devices, has been widely investigated. A skyrmion can be nucleated by conversion from domain wall pairs, local spin injection, local heating, and spin waves. Then, we focus on the current induced skyrmion motion and compare the two different torques:the spin transfer torque and the spin orbit torque. To read the data, it is necessary to detect skyrmions electrically. One way is to measure the topological Hall effect in a Hall bar. More commonly, skyrmions can be detected through magnetoresistance effects, i.e., giant magnetoresistance/anisotropic magnetoresistance, tunnel magnetore sistance, and non-collinear magnetoresistance, in a junction geometry. For manipulation, it is mainly demonstrated by the voltage controlled magnetic anisotropy (VCMA). Finally we discuss several representative skyrmionic nano-devices in memory, logic, and neuromorphic applications. The magnetic tunnel junction and the racetrack are two common designs for skyrmionic memory devices. The former can store multiple values in one bit, and the latter can realize fast and efficient data transmission. To control the skyrmionic data in these memories, the VCMA effect is one of the promising approaches, which is used in several designs. For the skyrmionic logic devices, they can be divided into two main types:the transistor and the logic gate. However, until now, these ideas are only demonstrated in simulation, and more efforts in experiment are needed. Besides, novel devices such as artificial synapses and neurons can be realized more naturally by skyrmion due to its particle-like property. In summary, skyrmionics is promising in several aspects, including performance improvement, emerging function and architecture design, and bio-inspired computing. Remarkable progress has been made in the past few years, however the device integration, the materials, and the data transmission still restrict its application. We hope this overview article may present a clear picture about skyrmionics and receive more attention, thus promoting its fast research and development in the future.