Brain-Computer Interface (BCI) is a powerful communication tool between users and systems, which enhances the capability of the human brain in communicating and interacting with the environment directly. Advances in neuroscience and computer science in the past decades have led to exciting developments in BCI, thereby making BCI a top interdisciplinary research area in computational neuroscience and intelligence. Recent technological advances such as wearable sensing devices, real-time data streaming, machine learning, and deep learning approaches have increased interest in electroencephalographic (EEG) based BCI for translational and healthcare applications. Many people benefit from EEG-based BCIs, which facilitate continuous monitoring of fluctuations in cognitive states under monotonous tasks in the workplace or at home. In this study, we survey the recent literature of EEG signal sensing technologies and computational intelligence approaches in BCI applications, compensated for the gaps in the systematic summary of the past five years (2015-2019). In specific, we first review the current status of BCI and its significant obstacles. Then, we present advanced signal sensing and enhancement technologies to collect and clean EEG signals, respectively. Furthermore, we demonstrate state-of-art computational intelligence techniques, including interpretable fuzzy models, transfer learning, deep learning, and combinations, to monitor, maintain, or track human cognitive states and operating performance in prevalent applications. Finally, we deliver a couple of innovative BCI-inspired healthcare applications and discuss some future research directions in EEG-based BCIs.