The most popular noninvasive Brain Robot Interaction (BRI) technology uses the electroencephalogram- (EEG-) based Brain Computer Interface (BCI), to serve as an additional communication channel, for robot control via brainwaves. This technology is promising for elderly or disabled patient assistance with daily life. The key issue of a BRI system is to identify human mental activities, by decoding brainwaves, acquired with an EEG device. Compared with other BCI applications, such as word speller, the development of these applications may be more challenging since control of robot systems via brainwaves must consider surrounding environment feedback in real-time, robot mechanical kinematics, and dynamics, as well as robot control architecture and behavior. This article reviews the major techniques needed for developing BRI systems. In this review article, we first briefly introduce the background and development of mind-controlled robot technologies. Second, we discuss the EEG-based brain signal models with respect to generating principles, evoking mechanisms, and experimental paradigms. Subsequently, we review in detail commonly used methods for decoding brain signals, namely, preprocessing, feature extraction, and feature classification, and summarize several typical application examples. Next, we describe a few BRI applications, including wheelchairs, manipulators, drones, and humanoid robots with respect to synchronous and asynchronous BCI-based techniques. Finally, we address some existing problems and challenges with future BRI techniques.