In functional materials, nanoscale phase boundaries exhibit exotic phenomena that are notably absent in their parent phases. Over the past two decades, much of the research into complex oxides (such as cuprate superconductors, CMR manganites and relaxor ferroelectrics) has demonstrated the key role that nanoscale inhomogeneities play in controlling the electronic and/or ionic structure of these materials. One of the key characteristics in such systems is the strong susceptibility to external perturbations, such as magnetic, electric and mechanical fields. A direct consequence of the accommodation of a large number of cationic substitutions in complex oxides is the emergence of a number of physical phenomena from essentially the same crystal framework. Recently, multiferroic behavior, which is characterized by the co-existence and potential coupling of multiple ferroic order parameters, has captured considerable worldwide research interest. The perovskite, BiFeO3, exhibits robust ferroelectricity coupled with antiferromagnetism at room temperature. A rather unique feature of this material system is its ability to "morph" its ground state when an external mechanical constraint is imposed on it. A particularly striking example is observed when a large (∼4 to 5%) compressive strain is imposed on a thin film through the epitaxial constraint from the underlying substrate. Under these conditions, the ground state rhombohedral phase transforms into a tetragonal-like (or a derivative thereof) phase with a rather large unit cell (c/a ratio of ∼1.26). When the epitaxial constraint is partially relaxed by increasing the film thickness, this tetragonal-like phase evolves into a "mixed-phase" state, consisting of a nanoscale admixture of the rhombohedral-like phase embedded in the tetragonal-like phase. Such a system gives us a new pathway to explore a variety of mechanical, magnetic and transport phenomena in constrained dimensions. This article reviews our progress to date in this direction and also captures some possible areas of future research. We use the electromechanical response and the magnetic properties as examples to illustrate that its novel functionalities are intrinsically due to the phase boundaries and not the constituent phases. The possible origin of the giant piezoelectric response and enhanced magnetic moment across the boundaries is proposed based on the flexoelectric and flexomagnetic effects.