Studies of interactions between surfaces immersed in a solution containing oppositely charged polyions are reviewed. Experimental as well as theoretical progress is discussed, focusing on underlying molecular mechanisms. * To whom correspondence should be addressed 1 particle interactions, on account of the steric repulsion that results as the polymer layers are compressed when two such particles approach. However, as the solvent gets poorer, which often can be regulated by changing the temperature or adding salt, these interactions may turn attractive, often resulting in flocculation, or the formation of a gel. 7 Ungrafted and non-adsorbing polymers tend to generate depletion attractions between the particles. If these "free" (ungrafted) polymers instead adsorb at the particle surfaces, the scenario is a bit more complex. Equilibrium interactions then tend to be overall attractive, with a free energy minimum stemming from the entropic increase that results when adsorbed chains are able to bridge across to a neighbouring particle. However, the attraction is generally short-ranged, and there is often a considerable free energy barrier at larger separations. In other words, such a dispersion may in practice be apparently (kinetically) stabilized by polymer addition. This is reminiscent to the barriers provided by electrostatic repulsion for charged particles (at low salt). Non-equilibrium phenomena are relevant also to the very interactions that the polymer give rise to. We shall discuss this in more detail below, but for now we note that finite configurational relaxation times, as well as diffusion limitations, may lead to polymer-mediated interactions that differ from those at true equilibrium. If so, it should be noted that fully relaxed states by definition have a lower free energy than their non-equilibrium corre