This chapter explores how internal model analysis enables more effective machine unlearning (MU) by leveraging structural, gradient-based, and attributional insights into model weights. While exact unlearning via full retraining guarantees faithful data removal, it remains computationally prohibitive for modern foundation models. Recent advances reveal that localizing the parameters most responsible for forgotten knowledge, via sparsity patterns, weight saliency, and attribution scores, can dramatically narrow the gap between approximate and exact unlearning while preserving model utility. We begin with model sparsification, where pruning redundant parameters reduces unlearning error and motivates sparsity-aware objectives. Building on this structural perspective, we then examine weight saliency, which uses gradient-based criteria to identify and update parameters most associated with harmful knowledge, achieving state-of-the-art results in both discriminative and generative tasks, including diffusion models. Finally, we introduce attribution-guided unlearning via bi-level optimization, providing a principled mechanism for quantifying parameter importance under utility constraints and delivering state-of-the-art performance for unlearning in large language models (LLMs).