The IV-VI semiconductors, and specifically the lead-salts (PbS, PbSe, and PbTe), are a natural choice for nanocrystal science. In nanocrystals, because of their narrow band gap, small effective masses, and large dielectric constants, they offer a unique combination of both strong confinement and strong dielectric contrast with their environment. Studying how these two effects modify optical and electrical properties of nanocrystals will be the topic of this dissertation. We begin with a summary of the synthesis of high-quality PbS and PbSe nanocrystals. Special care is taken to explain the chemical procedures in detail to an audience not expected to have significant prior chemistry knowledge. The synthesized nanocrystals have bright and tunable emission that spans the edge of the visible to the near-IR spectrum (700-1800 nm), and they are capped with organic ligands making them easily adaptable to different substrates or hosts . This combination of high optical quality and flexible device engineering make them extremely desirable for application. Moving beyond single-material nanocrystals, we next explore nanocrystal heterostructures, specifically materials with a spherical core of one semiconductor and a shell of another. Core-shell structures are commonly used in nanocrystals as a method to separate the core material, where the electrons and holes are expected to stay, from interfering effects at the surface. This typically results in improvements in stability and fluorescence quantum efficiency. To that end, we develop a model to explain how confinement plays out across abrupt changes in material, focusing on the optical and electrical properties of recently synthesized PbSe/PbS core-shell quantum dots. We show that for typical sizes of these nanocrystals, a novel type of nanocrystal heterostructure is created, where electrons and holes extend uniformly across the abrupt material boundary, and the shell does not act as a protecting layer. For very large sizes not yet achievable, we expect that the electron and hole will separate in different layers, with potentially measurable effects. Comparisons are made to optical and electrical measurements on these structures, showing good agreement. Next, we explore how shape can impact nanocrystal properties, on top of their intrinsic size or material dependence. By looking at cylindrically shaped nanocrystals, called "nanorods," with aspect ratios 10, we explore how having a slightly extended dimension can impact nanocrystal properties. A model is developed to explain their electronic structure, with surprising results. Foremost is that along the extended dimension, electrons and holes are strongly electrically bound, not with each other directly, but with their image charges in the outer host dielectric material. Nevertheless, the energy spectra of the excitons remains nearly hostindependent, with the effects of this strong binding instead seen in a redistribution of transition oscillator strength. To test the model, we develop a novel synthesis of high quality PbSe nanorods, and find good agreement with measured absorption spectra. Finally, we present a study on the transfer of charge into and out of a nanocrystal. By modeling the charge transfer process within a modified Marcus Theory, we isolate the relevant parameters that can be used to control the rate of transfer. Primary among these are the values of the quantum dot energy levels, and the electrostatic charging energy of the acceptor. We vary the former by changing the quantum dot size, and the latter by varying the host dielectric constant. To test the model, we chemically bind a small molecular acceptor molecule to the surface of PbS nanocrystals and use transient fluorescence to measure the rate of charge transfer. Both the dependence of the rate on quantum dot size and host dielectric constant show good agreement with the model.