In many practical situations, bubbles are dispersed in a liquid phase. The understanding and the modeling of bubbly flows is therefore a major issue for many applications including chemical engineering (bubble columns), water treatment (oxygenation and purification), nuclear industry (steam generators, accidental depressurizations), naval transport (skin drag reduction) and medicine (contrast agent, microbubbles bursting). Bubbly flows result from the twoway coupling between a liquid and bubbles that are randomly distributed over space. The specific properties of the bubbles make their dynamics very rich. Bubbles are inertialess and deformable, which complicates the expression of the hydrodynamic forces that act on them. They are compressible, which causes bubbly flows to be complex media for pressure waves and allows cavitation to occur. The interface properties are influenced by the presence of surfactant molecules that may be adsorbed at the bubble surface. In addition, the size of the bubbles is often not small compared to the characteristic length scales of the flow and buoyancy forces play a significant role. This implies to consider a large range of length scales and causes the generation of a strong agitation known as pseudo-turbulence. Owing to their complexity, different approaches have to be combined to deal with the different aspects of bubbly flows. Numerical simulations are particularly well suited to investigate phenomena at the bubble scale. In this course, the fundamentals of the numerical simulation of bubbles will be presented and, in particular, the hydrodynamic loads acting on a bubble will be discussed in detail. Collective effects are better addressed by experimental investigations. A review of advanced experimental techniques (Highspeed imaging, Particle Image Velocimetry, 3D Particle Tracking Velocimetry…) will be proposed and the dynamics of a swarm of rising bubbles will be described for both Newtonian and non-Newtonian liquids. Theoretical methods are also of great help in the study of bubbly flows. Theoretical expression of hydrodynamic forces on a single bubble will be presented for large or small Reynolds numbers. Averaged equations will be derived to handle the stochastic character of flows involving many bubbles. The objective is to provide stateof-the-art information on bubbly flow. The principal methods of investigations will be exposed and illustrated. The flow will be considered at different scales, from that of a single bubble to that of a bubble swarm. Major results concerning the dynamics of bubbly flows will be presented as well as several modern applications. The course is addressed to PhD students, young and senior researchers, or practicing engineers, involved in Chemical Engineering, Mechanical Engineering or Fluid Dynamics. Since it does not focus on a particular technique (numerical, experimental or theoretical), it should be of interest for a large audience.