A well-known neurophysiological marker that can easily be captured with electroencephalography (EEG) is the so-called P300: a positive signal deflection occurring at about 300ms after a relevant stimulus. This brain response is particularly salient when the target stimulus is rare among a series of distracting stimuli, whatever the type of sensory input. Therefore, it has been proposed and extensively studied as a possible feature for direct brain-computer communication. The most advanced non-invasive BCI application based on this principle is the P300-speller. However, it is still a matter of debate whether this application will prove relevant to any population of patients. In a series of recent theoretical and empirical studies, we have been using this P300-based paradigm to push forward the performance of non-invasive BCI. This paper summarizes the proposed improvements and obtained results. Importantly, those could be generalized to many kinds of BCI, beyond this particular application. Indeed, they relate to most of the key components of a closed-loop BCI, namely: improving the accuracy of the system by trying to detect and correct for errors automatically; optimizing the computer's speed-accuracy trade-off by endowing it with adaptive behavior; but also simplifying the hardware and time for set-up in the aim of routine use in patients. Our results emphasize the importance of the closed-loop interaction and of the ensuing co-adaptation between the user and the machine whenever possible. Most of our evaluations have been conducted in healthy subjects. We conclude with perspectives for clinical applications.