  In the first part of this survey we give a modernised exposition of the
structure of the special unitary bordism ring, by combining the classical
geometric methods of Conner-Floyd, Wall and Stong with the Adams-Novikov
spectral sequence and formal group law techniques that emerged after the
fundamental 1967 work of Novikov. In the second part we use toric topology to
describe geometric representatives in SU-bordism classes, including toric,
quasitoric and Calabi-Yau manifolds.
