This paper concerns the theory behind developing a brain computer interface (BCI) and the applications of such a system. Signal acquisition methods such as Functional Magnetic Resonance Imaging (fMRI), Near-Infrared Spectroscopy (NIRS), Magnetoencephalography (MEG), Electrocorticography (ECoG), and Electroencephalography (EEG) are discussed. There is also a review of the different types of Event Related Potentials (ERP) and signal extraction methods for generating filters from the captured data to generate a model for a BCI. Finally, this paper covers a review of notable BCIs that are being utilized in a wide range of applications and gives a working example using BCILAB to generate results from a sample data set using the techniques discussed in the paper.