In the third chapter of my diploma thesis some basic principles of complex fluids and mathematical models for their modelling are presented. The fourth chapter concentrates on the field of microfluidics, microfluidic devices and transport phenomena in microfluidics. In the chapter I also present different materials and methods for fabrication of microfluidic devices. In the chapter five the main goal was to present passive and active micromixers and their use in microfluidics. The last chapter of my diploma thesis was driven by research on multiphase flow of fluids. I also focused my research on summarizing literature on the formation of instabilities in the multiphase flow, from which I concluded that difference in viscosity and density of two fluids is one of the main reasons for formation of instabilities in a fluid network. From literature review I concluded that instabilities can be either enhanced or weakened by adjusting volume fraction of inlet fluids and flow rate. The main method of my research was literature review from articles, as well as books.