Motor brain-computer interface (BCI) refers to the BCI that decodes voluntary motion intentions from brain signals directly and outputs corresponding control commands without activating peripheral nerves and muscles. Motor BCIs can be used for the restoration, compensation, and augmentation of motor function by activating the neuromuscular circuit and facilitating neural plasticity. The essential applications of motor BCIs include neurorehabilitation and daily-life assistance for motor-impaired patients. In recent years, studies on motor BCIs mainly concentrate on neural signatures, movement decoding, and its applications. In this review, we aim to provide a comprehensive review of the state-of-the-art research of electroencephalography (EEG) signals-based motor BCIs for the first time. We also aim to give some insights into advancing motor BCIs to a more natural and practical application scenario. In particular, we focus on the motor BCIs for the movements of the upper limbs. Specifically, the experimental paradigms, techniques, and application systems of upper-limb BCIs are reviewed. Several vital issues in developing more natural and practical upper-limb motor BCIs, including developing target-users-oriented, distraction-robust, and multi-limbs motor BCIs, and applying fusion techniques to promote the natural and practical motor BCIs, are discussed.