A growing number of affective computing researches recently developed a computer system that can recognize an emotional state of the human user to establish affective human-computer interactions. Various measures have been used to estimate emotional states, including self-report, startle response, behavioral response, autonomic measurement, and neurophysiologic measurement. Among them, inferring emotional states from electroencephalography (EEG) has received considerable attention as EEG could directly reflect emotional states with relatively low costs and simplicity. Yet, EEG-based emotional state estimation requires well-designed computational methods to extract information from complex and noisy multichannel EEG data. In this paper, we review the computational methods that have been developed to deduct EEG indices of emotion, to extract emotion-related features, or to classify EEG signals into one of many emotional states. We also propose using sequential Bayesian inference to estimate the continuous emotional state in real time. We present current challenges for building an EEG-based emotion recognition system and suggest some future directions.