Bhabha scattering is the process of choice for luminosity measurements
at all electron positron colliders, among which there is the proposed
International Linear Collider (ILC). Therefore, Bhabha scattering
plays a crucial role in the study of the phenomenology of elementary
particles.  In this seminar we motivate and present the calculation of
next-to-next-to-leading order (NNLO) corrections to the Bhabha
scattering differential cross section in QED. We review the results
that became available in the last few years and describe in some
detail the calculational methods which were employed to obtain these
results.