Cilia are tiny hair-like structures that cover the surfaces of biological cells. One of their functions is to generate flow. Artificial cilia are mechanical actuators that are designed to mimic the motion of natural cilia in order to create fluid transport in microchannels. These fluid propulsion systems have potential for application in lab-on-a-chip devices that are used, e.g., for point-of-care diagnosis. The artificial cilia can be actuated through various means such as light, magnetic fields and electric fields. One of the main challenges in the design of artificial cilia is to find the cilia geometry and spacing, microchannel geometry, external actuation field, and frequency of operation, for which the fluid transported and the pressure generated are maximal. Various researchers have attempted to provide answers to these questions using computational models and experimental studies. The main feature of the computational models is that they accurately capture the interaction between the external actuation field (such as electric or magnetic fields), the motion of the artificial cilia and the fluid flow. In this chapter, we (i) give a brief overview of the existing modeling approaches, (ii) give an in-depth description of a recently developed modeling framework, and (iii) provide an overview of the most important results and insights that has led to our current understanding of the fluid propulsion using magnetically driven artificial cilia.