A wide variety of materials with nanometre dimensions are increasingly explored for photonic applications. Among them, semiconductor nanocrystals (NCs) are very promising for a variety of uses, including light emission devices (LEDs), lasers, detectors, photovoltaic cells, biological labelling and sensing [1]. Key advantage of NCs is the possibility to tailor their optical response by controlling the electronic structure (“wave function engineering”) through the choice of composition, size and shape. Significant and interesting results have been obtained with heterostructured and doped NCs. Beyond single wavelength tuneable band-edge emission, other regimes have been demonstrated such as intragap emission, simultaneous emission on two different wavelengths, amplified spontaneous emission and laser emission.The luminescent properties are governed by exciton decay, which can proceed through radiative or nonradiative pathways, following different routes. The study of exciton dynamics can allow elucidating the processes connected to single or dual emission and to optical gain. This, in turn, can lead to the identification of the functional and structural characteristics that are responsible for these behaviors. Exciton relaxation occurs on picosecond timescales, so ultrafast optical techniques are required to perform these studies.In this talk, we present studies carried out by ultrafast pump-probe spectroscopy technique, with 100-fs time resolution, on CdSe/CdS and PbS/CdS heterostructured NCs, with different geometries (core/shell, dot-in-rod, dot-in-bulk, with sharp or graded interface) [2-6] and CdSeS and CdZnSe doped NCs [7,8]. These NCs are optically active in the visible and near-infrared spectral region, show single and dual colour photoluminescence emission, optical gain, laser emission and intragap emission [2-9]. The analysis of the experimental data allowed us to unravel the decay processes: the initials take place in a few ps, leading to the ultimate emitting state whose lifetime can extend to hundreds of ps to few ns, allowing for efficient luminescence and optical gain.Our data on heterostructures allowed us to clarify the role of the volume and of the shape of the outer component and the effect of the interface [2-4]. We found that dual emission is possible for both thick and thin quantum-confined shells, and for different interfaces. We studied the decoupling of excitons lying in the two different component of the NC (core exciton and shell exciton) and we revealed the evolution of the exciton barrier known as dynamic hole-blockade effect. We showed that these phenomena are strictly connected to dual emission and optical gain and we identified the condition for their maximum efficiency, in term of band alignment and band transitions. Our results provide a comprehensive understanding of the physical phenomena governing dual-emission mechanisms, suppression of Auger recombination, optical gain and laser emission in heterostructured NCs.Experiments on CdZnSe NCs doped with Mn and on CdSeS NCs engineered with sulfur vacancies, enabled us to disclose donor and acceptor localized states in the band gap. We observed the carrier dynamics responsible for intragap emission which is associated to the emergence of a transient Mn3+ state [7], in the first case, and to a donor state below the conduction band introduced by sulfur vacancies [8], in the latter case.In conclusion, the study of the exciton dynamics in different NCs allowed us to elucidate the relation between structural-morphological characteristics (shape, volume, and interface) and unconventional emission capabilities (dual emission and optical gain) in heterostructures and the photophysics of electronic states introduced by doping. This knowledge is very important to control NC functionalities toward new multilevel electronic or photonic schemes and in applications such as lasers [9], photoelectrochemical (PEC) cell [10], white light emission [11], ratiometric sensing [12].[1] P. V. Kamat and G. D. Scholes, J. Phys. Chem. Lett. 7, 584 (2016)[2] G. Sirigu et al., Phys. Rev. B 96, 155303 (2017)[3] V. Pinchetti et al., ACS Nano 10, 6877-6887 (2016)[4] H. Zhao et al., Nanoscale 8, 4217-4226 (2016)[5] M. Zavelani-Rossi et al., Nano Lett. 10, 3142-3150 (2010)[6] R. Krahne et al., Appl. Phys. Lett. 98, 063105 (2011)[7] K. Gahlot et al., ACS Energy Lett. 4, 729−735 (2019)[8] F. Carulli et al., Nano Lett. 21, 6211−6219 (2021)[9] M. Zavelani-Rossi et al., Laser & Photonics Reviews 6, 678-683 (2012)[10] L. Jin et al., Nano Energy 30, 531-541 (2016)[11] S. Sapra et al., Adv. Mater. 19, 569 (2007)[12] J. Liu et al., ACS Photonics, 2479 (2019)