This thesis presents an experimental study of the time-resolved optical response of three different nanoscale systems: CdSe and PbSe quantum dots, and silver triangular nanoplates. The first part of the thesis is devoted to the understanding of the effects of quantum confinement on carrier-carrier interaction in a "model" system: CdSe quantum dots. This issue is addressed by investigating the evolution of the early-time fluorescence spectra of quantum dots of different sizes and lattice structure. The experiment is performed using a femtosecond photoluminescence up-conversion technique, with polychromatic detection. The transient photoluminescence spectra reveal the emission from short-lived multiexciton states. By combining a detailed spectral and kinetic analysis, it is possible to: (i) evaluate the binding energies of these states and therefore acquire insight on the strength of multi-particle interactions, (ii) understand how these interactions affect the lifetime of multiexciton states and, (iii) infer their mechanisms of formation upon optical excitation. We find that confinement-enhanced Coulomb interaction between carriers leads to large binding energies (> 20 meV) and activates efficient Auger-type recombination. This last mechanism points to somewhat different carrier interactions with respect to bulk semiconductors. Surprisingly, we observe that "tailoring" the lattice structure of the quantum dot does not significantly affect the spectral and dynamic properties of multiexciton states. The second part of the thesis addresses the effects of quantum confinement in semiconductor nanocrystals from a slightly different point of view, by investigating PbSe quantum dots. This material is supposed to exhibit a mirror-like, sparse, energetic structure due to extreme quantum confinement which should profoundly alter the carrier relaxation dynamics. We analyze the inter- and intra-band relaxation by combining several techniques. In order to characterize the evolution of the particles luminescence from the nanosecond to the femtosecond range, we perform time-correlated single photon counting and femtosecond near-infrared photoluminescence up-conversion measurements. The results are compared with near infrared, broadband transient absorption measurements. Overall, we observe extremely fast intraband relaxation times, on sub-ps time scales, slightly increasing with decreasing dot size. From our analysis we can estimate a weak electron-phonon coupling between excited states, and we observe that surface mediated relaxation does not play a relevant role in this system. The third part of this work concerns the investigation of the time-resolved optical response of silver triangular nanoplates. The optical response provides fundamental information about the relaxation mechanisms of plasmons, electrons and phonons in metal nanocrystals, and access to the mechanical properties of metal nanoparticles. The anisotropy of the system under study is found to influence the physical properties: we observe for the first time two different excitation mechanisms of mechanical vibrations. In order to disentangle homogenous and inhomogeneous contributions, we present a model which takes into account a realistic distribution of particle size and shape, and which is able to capture the relevant dynamics in these complex systems.