Algebraic geometry provides powerful tools for embedding the Standard Model of particle physics into string theory. The Standard Model encodes much of what we know about particle physics: the three forces (electromagnetism, weak and strong nuclear forces) associated with the gauge group U(1) x SU(2) x SU(3); the particles: quarks (which make up protons and neutrons) and leptons (electrons, neutrinos), each recurring in three "generations", plus the elusive Higgs particle; and the precise rules that determine which interactions of particles and forces can occur and which are excluded. The best hope for combining this tremendously successful quantum theory of the three forces with the remaining force, gravity (i.e. with general relativity), is based on String Theory and M-Theory. In this expository talk I will survey some recent breakthroughs and open questions in deriving versions of the Standard Model, via a "Grand Unified Theory", from heterotic string theory and F-theory. The geometry underlying the heterotic version amounts to constuction of stable vector bundles over Calabi-Yau threefolds and determination of their cohomology. These CYs often have either an elliptic fibration (leading to Grand Unified theories) or a genus one fibration (leading to Standard-Model-like theories). The F-theory constructions are based on Calabi-Yau fourfolds.