Recently, strain engineering has been shown to be a powerful and flexible means of tailoring the properties of ABO 3 perovskite thin films. The effect of epitaxial strain on the structure of the perovskite unit cell can induce a host of interesting effects, these arising from either polar cation shifts or rotation of the oxygen octahedra, or both. In the multiferroic perovskite bismuth ferrite (BiFeO 3 -BFO), both degrees of freedom exist, and thus a complex behaviour may be expected as one plays with epitaxial strain. In this paper, we review our results on the role 2014 The Author(s) Published by the Royal Society. All rights reserved. of strain on the ferroic transition temperatures and ferroic order parameters. We find that, while the Néel temperature is almost unchanged by strain, the ferroelectric Curie temperature strongly decreases as strain increases in both the tensile and compressive ranges. Also unexpected is the very weak influence of strain on the ferroelectric polarization value. Using effective Hamiltonian calculations, we show that these peculiar behaviours arise from the competition between antiferrodistortive and polar instabilities. Finally, we present results on the magnetic order: while the cycloidal spin modulation present in the bulk survives in weakly strained films, it is destroyed at large strain and replaced by pseudo-collinear antiferromagnetic ordering. We discuss the origin of this effect and give perspectives for devices based on strain-engineered BiFeO 3 .