The flow behavior of droplet-based liquid-liquid systems, such as emulsions, polymer blends, and foodstuff, which are ubiquitous in everyday life, has attracted scientific interest in different disciplines. In this review, we focus on the pressure-driven confined flow behavior of isolated droplets in circular and rectangular cross-section channels, which are valuable model geometries to gain insight into more complex flow conditions found in industrial applications. The effect of the relevant nondimensional parameters governing droplet deformation and breakup, such as viscosity ratio, capillary number, and ratio of droplet to tube radius, is presented both for axisymmetric and off-axis droplets, including cross-stream migration. The role of surfactants is also discussed. Ongoing research directions include the field of microfluidics techniques, where confined flow geometries can be exploited to manipulate droplets with a variety of possible applications.