Quantum confined semiconductor nanoparticles, such as colloidal quantum dots, nanorods and nanoplatelets have broad extended absorption spectra at energies above their bandgaps. This means that they can absorb light at high photon energies leading to the formation of hot excitons with finite excited state lifetimes. During their existence, the hot electron and hole that comprise the exciton may start to cool as they relax to the band edge by phonon mediated or Auger cooling processes or a combination of these. Alongside these cooling processes, there is the possibility that the hot exciton may split into two or more lower energy excitons in what is termed carrier multiplication (CM). The fission of the hot exciton to form lower energy multiexcitons is in direct competition with the cooling processes, with the timescales for multiplication and cooling often overlapping strongly in many materials. Once CM has been achieved, the next challenge is to preserve the multiexcitons long enough to make use of the bonus carriers in the face of another competing process, non-radiative Auger recombination. However, it has been found that Auger recombination and the several possible cooling processes can be manipulated and usefully suppressed or retarded by engineering the nanoparticle shape, size or composition and by the use of heterostructures, along with different choices of surface treatments. This review surveys some of the work that has led to an understanding of the rich carrier dynamics in semiconductor nanoparticles, and that has started to guide materials researchers to nanostructures that can tilt the balance in favour of efficient CM with sustained multiexciton lifetimes.