  In this survey, we give an overview of Brieskorn manifolds and varieties, and
their role in contact topology. We discuss open books, fillings and invariants
such as contact and symplectic homology. We also present some new results
involving exotic contact structures, invariants and orderability. The main tool
for the required computations is a version of the Morse-Bott spectral sequence.
We provide a proof for the particular version that is useful for us.
