Microfluidic systems allow (bio)chemical processes to be miniaturized with the benefit of shorter time-to-result, parallelism, reduced sample consumption, laminar flow, and increased control and efficiency. However, such miniaturization inherently limits the size of the solid objects that can be processed and entails new challenges such as the interfacing of macroscopic samples with microscopic conduits. Here, we report a microfluidic probe (MFP) that overcomes these problems by combining the concepts of 'microfluidics' and of 'scanning probes'. Here, liquid boundaries formed by hydrodynamic forces underneath the MFP confine a flow of processing solution and replace the solid walls of closed microchannels. The MFP is therefore mobile and can be used to process large surfaces and objects by scanning across them. We illustrate the versatility of this concept with several examples including protein microarraying, complex gradient-formation, multiphase laminar-flow patterning, erasing, localized staining of cells and the contact-free detachment of a single cell. Many constraints imposed by the monolithic construction of microfluidic channels can now be circumvented using an MFP, opening up new avenues for microfluidic processing.