Understanding the nonlinear vibration behavior of structures is critical to ensuring reliability and improving efficiency. Jointed connections, integral to assembled structures, introduce contact and friction resulting in nonlinear vibration behavior. Specifically, properties of linear modal analysis including constant modal frequencies and damping and the decoupling of modes break down in the case of nonlinear vibration. Of interest here, modal interactions occur when multiple nonlinear modes respond simultaneously modifying the total response characteristics, potentially increasing vibration amplitudes and causing structural failures. An understanding of modal interactions is predicated on capturing the nonlinear effects of friction in joints, so this thesis investigates physics-based friction modeling to numerically simulate responses of benchmark jointed structures. To address computational costs, a new method is developed to analyze modal interactions utilizing the developed friction model. In the case of a single mode, frictional contact results in a decrease in modal frequency and an increase in modal damping as the vibration amplitude increases. This behavior is well captured by the proposed friction modeling approach. Beyond the single mode case, the state of the art for modeling modal interactions is thoroughly reviewed, and open challenges are discussed. To better understand modal interactions, a numerical method termed variable phase resonance nonlinear modes (VPRNM) is proposed for tracking superharmonic resonances, a specific type of modal interaction. Superharmonic resonances occur at steady-state when a mode responds in resonance at an integer multiple of the forcing frequency (e.g., with amplitude on the order of the response at the forcing frequency). When a superharmonic resonance occurs simultaneously with a primary resonance, the response is further complicated and termed an internal resonance. Utilizing VPRNM, a reduced order modeling approach (VPRNM ROM) is proposed to reconstruct frequency response curves with significantly reduced computational cost compared to existing approaches. This thesis compares the proposed modeling approaches to new experimental results for the Half Brake-Reuss Beam, a benchmark jointed structure. Overall, this thesis provides significant insights into the phenomena of modal interactions for jointed connections and approaches for computationally efficiently modeling such interactions.