In contrast to conventional microfluidics, where liquids are typically manipulated within closed channels, open-space microfluidics has emerged as a new class of techniques that are well suited for ver-satile interaction with biological substrates. In particular, non-contact microfluidic technologies, so called liquid scanning probes, allow to compartmentalize otherwise fully miscible liquids in the "open space" on immersed surfaces and are starting to translate from academic research to commercial products. One such family of liquid scanning probes localize liquids using hydrodynamic flow confinement (HFC). Such HFC-based liquid scanning probes enable controlling the physico-chemical microenvironments of im-mersed biological surfaces and thus are highly-suited for additive and subtractive patterning of surfaces and for interactions with cells on surfaces. This thesis presents a scaling analysis of HFC-based liquid scanning probes in the context of one such technology, the microfluidic probe (MFP). The analysis along each scaling dimension is based on first principle models and validated in the context of relevant biological applications. To improve the efficiency in the use of expensive reagents, a method to recirculate a µl-scale volume of liquid within an HFC was developed. The concept was demonstrated in the context of forming a protein bio-array comprising 170 deposition sites using only 1.7µl of protein-solution. The consumption of proteins was reduced by a factor of 10 compared to deposition without recirculation. For HFC-based interaction at larger length-scales, as needed in diagnostics, we further developed multi-layered vertical probe heads enabling novel aperture geometries and arrangements. These allow the homogeneous and multiplexed incubation of tissue sections with primary antibody solutions at processing times of a few minutes. Horizontal probe head were used to implement a multi-step protocol for immunohistochemical analysis of samples with an optimized trade-off between incubation time, signal levels and signal contrast. Another key aspect in the translation of HFC-based liquid scanning probes is to counter two main failure modes impending their long-term operation: 1) obstructions of apertures and channels by debris and, 2) deviations from the ideal probe-sample distance. Both these failure modes can be addressed via a simple design element, a microfluidic bypass channel. A liquid-filled, resistive bypass in the case of an obstruction intrinsically re-routes flow-paths and avoids spills. An air-filled, capacitive bypass allows to track the probe-sample distance up to 25µm by observing the phase shift in transduced pressure pulses. Towards enabling interactive microfluidic experimentation, we propose an HFC-based approach to form and re-configure flow trajectories of reagents, so-called virtual channels. Provided enough degrees of freedom in flow control, i.e. independently controllable injection and aspiration channels, user defined reagent-flow paths can be matched at high fidelity in real-time. We demonstrate the concept by using virtual channels to form patterns of proteins on a glass slide and by local lysis and staining of cell block sections. The concepts, methods and devices presented in this dissertation contribute to the development of hydrodynamic confinements in the "open space" and, are critical elements in the translation of HFC-based liquid scanning probes to applications in the life sciences.