  Vector bundle cohomology represents a key ingredient for string
phenomenology, being associated with the massless spectrum arising in string
compactifications on smooth compact manifolds. Although standard algorithmic
techniques exist for performing cohomology calculations, they are laborious and
ill-suited for scanning over large sets of string compactifications to find
those most relevant to particle physics. In this article we review some recent
progress in deriving closed-form expressions for line bundle cohomology and
discuss some applications to string phenomenology.
