Brain-Computer interfaces (BCIs) enhance the capability of human brain activities to interact with the environment. Recent advancements in technology and machine learning algorithms have increased interest in electroencephalographic (EEG)-based BCI applications. EEG-based intelligent BCI systems can facilitate continuous monitoring of fluctuations in human cognitive states under monotonous tasks, which is both beneficial for people in need of healthcare support and general researchers in different domain areas. In this review, we survey the recent literature on EEG signal sensing technologies and computational intelligence approaches in BCI applications, compensating for the gaps in the systematic summary of the past five years. Specifically, we first review the current status of BCI and signal sensing technologies for collecting reliable EEG signals. Then, we demonstrate state-of-the-art computational intelligence techniques, including fuzzy models and transfer learning in machine learning and deep learning algorithms, to detect, monitor, and maintain human cognitive states and task performance in prevalent applications. Finally, we present a couple of innovative BCI-inspired healthcare applications and discuss future research directions in EEG-based BCI research.