Metals with excitonic instabilities are multiband systems with significant electron-electron interaction. The electronic transport in such systems is affected by collective fluctuations of the electrons, leading to anomalous features in the measured transport coefficients. Many of these anomalies have not been well understood because the transport mechanisms in these systems tend to be rather complex. The complexity arises, on the one hand, from the multiband nature and, on the other, from the anisotropic scattering of electrons accompanied by emitting or absorbing collective fluctuations. Previous works considering scattering due to collective fluctuations have mainly focused on single-band systems, for example in the context of the normal-state transport in cuprates. The recent discovery of high-temperature superconductivity in iron pnictides has renewed the interest in multiband systems. Exploring the transport mechanisms in multiband systems, I find some interesting new aspects, which do not occur in single-band systems. In particular, anisotropic scattering in a model with electronlike and holelike Fermi surfaces can lead to a negative conductivity contribution of the minority carriers, i.e., in an electric field, the minority carriers drift in the direction opposite of what one would expect based on their charge. I show that this effect can explain a reduced magnetoresistance in connection with an enhanced Hall coefficient, which has been measured in pnictides. Of particular interest are multiband models with hot spots on the Fermi surface, in part because of their relevance for the iron pnictides. Hot spots are states with enhanced scattering and therefore reduced excitation lifetimes. In single-band systems, the hot spots are found to have a much lower contribution to the total conductivity than other parts of the Fermi surface, which leads to the so-called hot-spot structure. I show that in the multiband case, the conductivity contributions are much more isotropic around the Fermi surface so that hot spots contribute to transport with a similar strength as other parts of the Fermi surface. I discuss this effect on the basis of an approximate analytical solution of the transport problem and numerically calculate the temperature dependence of several transport coefficients. It turns out that in the nematic phase of iron pnictides, the unexpectedly strong conductivity contribution of hot spots can explain the puzzling behavior of the resistive anisotropy. I show that the experimental observations can be explained within a scenario in which the anisotropy is mainly due to the broken symmetry of the spin-fluctuation spectrum in the nematic phase. In the spin-density-wave state, strongly anisotropic scattering can arise due to the propagating magnons. Using a two-band model relevant for iron pnictides, I find that this scattering can lead to an unusual interruption of the orbital motion of electrons in the magnetic field. As a consequence, the low-field magnetoresistance is linear with an alternating sign of the slope as a function of the direction of the current. In strong magnetic fields, the interrupted orbital motion makes the system unstable, which is characterized by a drop of the resistivity to zero.