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Understanding the fundamental properties of electrochemical systems, especially at the microscopic level, requires advanced tools combining electrochemical microscopy and scanning probe techniques with mathematical modeling for the quantification of the physicochemical characteristics of these environments. Comparison, analysis and sometimes calibration of the experimental results with theoretically predicted values is an indispensable strategy of any scientific method. In this thesis, experimental investigations are complemented with computations and numerical simulations. Novel microfluidic probes for scanning electrochemical microscopy (SECM) were developed. These soft SECM probes are equipped with an ultramicroelectode and integrated counter-reference electrode for characterizing the electrochemical reactivity of the substrate. They also incorporate microfluidic channels for delivery and removal of electrolyte solutions to and away from the probe tip allowing SECM experiments to be carried out on initially dry substrates. Additional integration of this concept with a chemical detection of the circulating electrolyte by means of mass-spectrometric analysis demonstrated the possibility to turn these microfluidic probes into a scanning tool for localized stimulation, control and read-out of chemical events occurring at interfaces. This work was also accomplished with two- and three- dimensional finite element modeling of the amperometric probe response under various geometrical arrangements taking into account microfluidic perturbations. Theoretical investigations of the capacitive properties of liquid/liquid interfaces were carried out taking into account the effect of smooth variation of permittivity across the liquid/liquid boundary. The width and symmetry of the resulting interphase were shown to be crucial characteristics for the variation of ion solvation within the interfacial region and fitting the experimental data with a finite element model was used to estimate the thickness of liquid/liquid junctions. Diode-like behavior of tapered charged nanopores was investigated by means of computing ion fluxes using a simple perm-selective approximation and more complicated finite element models taking into account a uniform surface charge density inside the conical pipettes. These simulations provided an insight on the mechanisms governing the rectifying behavior of such systems under various circumstances, i.e. geometrical arrangement, electrolyte concentrations and different electrical potential/voltage scan rate conditions, proving the existence of a perm-selective barrier attributed to diffuse layer overlapping inside the charged nanopore. Finally, theoretical investigations of the analytical characteristics of solid phase extraction-gradient elution-mass spectrometry (SPE-GEMS) technique for proteomics were performed. The computations were used to optimize the experimental conditions and to estimate performance aspects of this microchip-based strategy by following sorption-desorption equilibria under gradient elution conditions, i.e. by varying solvent strength.