In this tutorial, I will present techniques for numerical simulation and modeling of phonon transport in a broad range of nanostructures, focusing primarily on modeling extrinsic and disorder effects such as grain/sample boundaries, interfaces, edges, and alloy mass disorder. The talk revolves around the phonon Boltzmann transport equation (pBTE), while the salient feature of the work is that it employs a full phonon dispersion combined with a momentum-dependent model of phonon boundary scattering. I will show that the thermoelectric response of SOI and Si-membrane-based nanostructures can be improved by employing the anisotropy of the lattice thermal conductivity, revealed in ultrathin SOI nanostructures due to the interplay between the anisotropy of the phonon dispersion and the strong boundary scattering. Furthermore, I explore the consequences of nanostructuring on silicon/germanium and Si/Si-Ge alloy superlattices, and show that the drastic reduction and high anisotropy of thermal conductivity in these structures comes from the increased interaction of lattice waves with rough interfaces and boundaries. Next, the tutorial will describe how super-diffusive transport emerges from alloy mass disorder scattering of phonons in nanowires. The tutorial will then turn to reduced thermal conductivity in both suspended and supported graphene nanoribbons (GNRs), which also exhibit strong anisotropy due to interaction of lattice waves with line edge roughness (LER) and the competition between LER and substrate scattering. Then my talk will review some recent work in length scaling of thermal conductivity in long graphene ribbons. Finally, I will discuss how my work extends to transport in nanocomposite and nanocrystalline materials as well as thermal rectifiers, paving the way toward more complete control over heat propagation at the nanoscale. I will close the loop with applications of my phonon transport models to studying thermal effects in ultrascaled gate-all-around MOS devices and nanomembrane detectors for mass spectroscopy.