A short review of recent progress in the field of multiferroic thin films and heterostructures is given. We focus on the bismuth iron oxide system due to its desirable properties, namely high ferroelectric Curie temperature and antiferromagnetic Neel temperature. Epitaxial growth of this model system in various crystallographic orientations has conclusively demonstrated the large ferroelectric polarization in this system. Piezoforce microscopy reveal a complex domain structure, especially on (100) SrTiO3 substrates. Electrical switching experiments show the co-existence of 71, 109 and 180 domain switching mechanisms in such films. Preliminary work has shown promise for electrically controllable exchange bias in ferromagnet-multiferroic heterostructures.