  We briefly review an algorithmic strategy to explore the landscape of
heterotic E8 \times E8 vacua, in the context of compactifying smooth Calabi-Yau
three-folds with vector bundles. The Calabi-Yau three-folds are algebraically
realised as hypersurfaces in toric varieties and a large class of vector
bundles are constructed thereon as monads. In the spirit of searching for
Standard-like heterotic vacua, emphasis is placed on the integer combinatorics
of the model-building programme.
