Colloidal nanocrystals (CNCs) are nanometer sized crystals grown in solution. Due to their size-tunable optical properties, CNCs have emerged as a novel material platform for numerous applications such as displays, photovoltaics, and biological tagging. However, the colloidal growth process results in an unavoidable distribution of CNC size that inhomogeneously broadens optical absorption/luminescence lineshapes. 2-D spectroscopy is a technique capable of circumventing inhomogeneous broadening by correlating absorption and emission dynamics. In this talk I will present our results from applying 2-D spectroscopy to CNCs at cryogenic temperatures. I will first discuss our experiments on conventional CdSe CNCs, in which we have simultaneously observed both bulk-like acoustic phonons and acoustic vibrations discretized by the nanocrystal geometry for the first time. Next, I discuss our experiments on perovskite CNCs, which are a new class of materials first synthesized in 2015. We demonstrate that coherences due to vibrational coupling exhibit anomalous dephasing dynamics, which we attribute to a cascaded coherence transfer process. Finally, I discuss our observations of coherences between so-called bright-triplet exciton states, which are robust at high temperatures and polarization-selective.