The mechanical strength of metals depends on their resistance against various microscopic deformation processes. In ductile metals, the most important process is shearing of the crystal lattice by dislocations. One of the fundamental aspects of dislocation motion is cross-slip of screw dislocations, the process by which they change their glide plane. In Face-Centered Cubic (FCC) metals, cross-slip is supposed to play a role in dislocation structuring, work hardening, recovery, fatigue, etc. Most prior studies on cross-slip in FCC metals focused on pure metals. There have been few studies of solute effects on cross-slip, which are important for engineering alloys. Here, the effects of substitutional solutes are studied using atomistic simulations and statistical modeling. In the first part of the thesis, the mechanism and energy of cross-slip of short (40 Burgers vectors long) dislocations in Ni-Al, Al-Mg and Cu-Ni alloys are determined using atomistic calculations. These calculations are carried out with real random alloys and with "average" alloys, where the real atom types are replaced by a single average type. By comparison, it is shown that cross-slip is controlled by fluctuations in the solute concentration, i.e. the activation energy for cross-slip is a distributed variable with a large variance around the mean value. The latter changes only little with concentration. Most importantly, activation energies that are significantly lower than the mean value can be observed in random alloys. A linear correlation between the activation energy and the energy difference between the state of the dislocation before and after cross-slip is observed. An analytical, parameter-free model of this energy difference is developed, which takes random changes in solute-dislocation and solute-solute binding energies into account. Thus, it is possible to predict the distribution of activation energies for nucleation of cross-slip. In the second part, cross-slip of long (10^2-10^3 Burgers vectors) dislocations is studied using a random walk model. Cross-slip is seen as a discrete process, where one Burgers vector long subsegments of the dislocation cross-slip one after another. Associated with each step is a random energy due to random changes in solute binding energies, as well as a deterministic energy change due to constriction formation and stress effects. The random walk model allows the calculation of the activation energy distribution for arbitrary dislocation lengths and stresses. Cross-slip of long dislocations is unlikely at zero stress, due to increasing frequency of high activation energies with increasing length. However, an external stress eliminates these high barriers. Cross-slip then becomes a weakest-link problem. Like in the case of short dislocations, activation energies that are significantly lower than average-alloy estimates can be observed in real random alloys.