This thesis presents an investigation of the magnetic properties and dynamics of maghemite (γ-Fe2O3) nanoparticle assemblies using atomistic spin dynamics simulations. The study focuses on the collective magnetic behavior that arises from the complex interplay between short intra-particle and long inter-particle interactions. The presence of vacancies in the maghemite structure introduces an inhomogeneous effective anisotropy unique to each nanoparticle. In triangular arrays, the interplay between surface effective anisotropy and dipolar interactions leads to the formation of magnetic domains, with domain size decreasing as surface anisotropy increases. The study first examines the magnetic ordering in triangular arrays of point dipoles. The simulations reveal ferromagnetic in-plane ordering with a six-fold anisotropy arising from the order-from-disorder effect, consistent with previous theoretical studies. The dipole interactions in the triangular array are then compared with those in maghemite nanoparticle arrays. While nanoparticle arrays with zero surface anisotropy exhibit similar behavior to point dipole arrays, the presence of surface anisotropy leads to the formation of magnetic domains, with domain size decreasing as surface anisotropy increases. The spin-wave spectra of point dipole arrays reveal weak longitudinal modes and more dominant transverse modes, with the dispersion relations agreeing well with theoretical calculations. Spin wave excitations in the nanoparticle arrays are explored using Fourier analysis. In addition to propagating spin waves, localized modes are observed, originating from the hopping of magnetization between energy minima at the individual nanoparticle level. Surface anisotropy introduces spectral gaps and increases spin wave frequencies of the transverse and longitudinal modes, with the frequency at zero wave-vector following a quadratic dependence on surface anisotropy strength for the transverse spin waves and a linear dependence on surface anisotropy for the longitudinal spin waves (for small values of surface anisotropy). The multiscale hierarchical model developed in this work captures the intricate interplay between intra-particle and inter-particle interactions. The atomistic simulations provide insights into the role of surface effects and defects in determining the magnetic properties of nanoparticle assemblies, highlighting the necessity of considering atomic-scale structure in the design and optimization of magnetic nanomaterials.