We survey certain accessible aspects of Grothendieck's theory of motives in
arithmetic algebraic geometry for mathematical physicists, focussing on areas
that have recently found applications in quantum field theory. An appendix (by
Matilde Marcolli) sketches further connections between motivic theory and
theoretical physics.Comment: LaTeX 35 pages, article by Abhijnan Rej with an appendix by
M.Marcolli. Version II/Final: cosmetic changes to bibliography, added a small
subsection on triangulated categories to section 6. Accepted for publication
in the MPIM-Bonn "Renormalization, combinatorics and physics" proceedings
volum
