Heterotic Models without Fivebranes

After discussing some general problems for heterotic compactifications involving fivebranes we construct bundles, built as extensions, over an elliptically fibered Calabi-Yau threefold. For these we show that it is possible to satisfy the anomaly cancellation topologically without any fivebranes. The search for a specific Standard model or GUT gauge group motivates the choice of an Enriques surface or certain other surfaces as base manifold. The burden of this construction is to show the stability of these bundles. Here we give an outline of the construction and its physical relevance. The mathematical details, in particular the proof that the bundles are stable in a specific region of the K\"ahler cone, are given in the mathematical companion paper math.AG/0611762.