Abstract: In the first part of the talk I will demonstrate how first-principles density functional theory (DFT) calculations can characterize the structural, energetic, electronic, and vibrational properties of atomically-thin black phosphorus (BP) and its nanostructures. Periodically hole patterning the material results in antidot lattices, where changing the geometric parameters controls the anisotropic quantum confinement strength, permitting quasi-continuous tunability of the electronic properties. Beyond BP there exists a recently predicted phosphorus allotrope, blue phosphorus (bP), which can be grown under particular conditions. By developing a new method for calculating the phonons of a continuous layer on a substrate, we showed that triangular single-layer bP on Au(111) is more stable than single-layer BP on Au(111) at all temperatures, in agreement with experiment. Furthermore, we captured non-linear phonon effects using ab initio molecular dynamics with our newly derived spectral lineshapes for the velocity autocorrelation method and, separately, many-body perturbation theory. The anharmonicity produces temperature dependent normal mode frequency shifts and finite lifetimes, which are in quantitative agreement with results from an experimental collaborator. The phonon lifetimes play a key role in the emergent macroscopic thermal conductivity. In the last segment I will discuss Floquet graphene antidot lattices, consisting of massless Dirac fermions in 2D excluded from a periodic array of nanoholes and coupled to intense radiation. The effective electronic properties of the system are encoded in the quasienergies, computed non-perturbatively via the Floquet matrix. For circular polarization with near-IR photon energies, we find the equilibrium semiconducting state can be transformed into Floquet Dirac, selectively dynamically localized, and Floquet semi-Dirac phases by suitable choice of intensity. Overall, the wide range of new results provides motivation to pursue applications in nanoelectronics, optoelectronics, and thermoelectric materials.