Already in 1968 one recognized that the transmission electron micro- scope could be used in a tomographic setting as a tool for structure determination of macromolecules. However, its usage in mainstream structural biology has been limited and one reason is the devastating combination of noisy data and incomplete data problems that leads to severe ill-posedness of the inverse problem. Despite these issues, the importance of electron tomography is beginning to increase, espe- cially in drug discovery. This review begins with a brief introduction to the model for image formation, i.e. the forward operator. Next, we state the difficulties and review some of the various attempts at overcoming those in solving the inverse problem.