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Control of the density of mobile charge carriers using electric fields is widely used in a variety of metal-insulator-semiconductor structures and is the governing principle behind the operation of field-effect transistors. Ferroelectric materials possessing a switchable and non-volatile polarization field can be used as insulating layers, revealing new opportunities for device applications. Advances in material processing and in particular complex oxide thin-film growth mean that high-quality field-effect devices can be based on ferroelectric/metallic oxide heterostructures. In addition, advances in local probe techniques such as atomic force microscopy allow them to be used in the imaging and study of small ferroelectric domain structures in bulk crystals and thin films. Meanwhile, scanning tunnelling microscopy and spectroscopy have established themselves as powerful techniques for atomic manipulation and nanometre-resolution electron tunnelling spectroscopy. Here, a scanning tunnelling microscope is used to investigate the ferroelectric field effect in all-perovskite heterostructures. Scanning tunnelling spectroscopy allows us to probe the local electronic properties of the polarized channel of a ferroelectric field-effect device as a function of the field orientation. This technique can be used to read and write ferroelectric field-induced regions with a size as low as 20 nm.