Microfluidic technology involves the manipulation of fluids (gas or liquid) in channels with dimensions lower than 1 mm, typically between 10-100 μm. Over the past 25 years, it has grown into a mature field. Because of the small channel dimensions, chemical process operations like mixing, reactions, dosing, and analyses have acquired substantial efficiency gains. However, one aspect remains underdeveloped: general techniques that enable downstream processing. One technique that has been reported to be promising for microfluidics, because of its universal applicability, is solvent extraction (SX). SX is the distribution of one or more chemical species (solutes) between two immiscible liquids because of a difference in solubility and is used to separate the solutes from each other. The problem, however, that exists in solvent extraction is that equilibrium is quickly obtained upon intensive dispersing, but this dispersion adversely affects the subsequent phase separation step. In this work, SX in membrane microcontactors was studied. With membrane contactors, the two liquids flow along each side of the membrane, preventing dispersion of the two solutions and consequently omitting a phase separation step. However, with current membrane contactors the equilibrium is attained slowly, typically in the range of hours. To speed this up, microfluidic technology was combined with the membrane contactor concept into a membrane microcontactor, enhancing the extraction rate substantially, completing SX in a matter of minutes. In the first part of the thesis, models were developed to describe the extraction rate, examine interface stability effects, and investigate spacer structuring to minimize membrane deflection and provide design guidelines. In the second part, the performance of the membrane microcontactor was examined both in the field of analytics (i.e. sample preparation) as in the field of reactive SX (i.e. hydrometallurgy). It was shown that challenging samples containing solids could be handled and reactive SX could be modeled and executed in a continuous fashion by regeneration of the extractant.