We study, within the tight-binding approximation, the electronic properties of a graphene bilayer in the presence of an external electric field applied perpendicular to the system -- emph{biased bilayer}. The effect of the perpendicular electric field is included through a parallel plate capacitor model, with screening correction at the Hartree level. The full tight-binding description is compared with its 4-band and 2-band continuum approximations, and the 4-band model is shown to be always a suitable approximation for the conditions realized in experiments. The model is applied to real biased bilayer devices, either made out of SiC or exfoliated graphene, and good agreement with experimental results is found, indicating that the model is capturing the key ingredients, and that a finite gap is effectively being controlled externally. Analysis of experimental results regarding the electrical noise and cyclotron resonance further suggests that the model can be seen as a good starting point to understand the electronic properties of graphene bilayer. Also, we study the effect of electron-hole asymmetry terms, as the second-nearest-neighbor hopping energies $t$ (in-plane) and $gamma_{4}$ (inter-layer), and the on-site energy $Delta$.
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