This paper presents approximation algorithms for network design problems under non-uniform fault models. The Survivable Network Design Problem (SNDP) is a well-studied problem, but its approximability is less understood in more complex models. The paper focuses on three models: flexible graph connectivity, bulk-robust network design, and relative survivable network design. In the flexible graph connectivity model, the edge set is partitioned into safe and unsafe edges. The goal is to design a network that has desired connectivity properties under the assumption that only unsafe edges up to a specific number can fail. The paper provides constant factor approximations for two special cases of this model: the single pair case and the global connectivity case. These results are based on an augmentation framework and decomposing the families of cuts that need to be covered into a small number of uncrossable families. In the bulk-robust model, the goal is to find a min-cost subgraph that remains connected after the failure of a specified number of edges in any scenario. The paper provides poly-logarithmic approximations for this model when the "width" of the instance is fixed. These results are obtained via two algorithmic approaches and have different tradeoffs in terms of the approximation ratio and generality. The paper also discusses the relative survivable network design model, which allows for higher connectivity even when the underlying graph has small cuts. The paper provides poly-logarithmic approximations for this model when the requirements are small. The paper shows that these problems admit poly-logarithmic approximation algorithms when the widths/connectivity requirements are small. The results are obtained via two different algorithmic approaches. The first uses a cost-sharing argument to show a reduction to the Hitting Set problem. The second uses natural LP relaxations and provides additional benefits such as upper bounds on the integrality gaps of the LP relaxations. The paper also extends these results to the group connectivity generalizations of the models. The results are obtained via a novel framework that combines ideas from the augmentation approach and LP relaxations. The paper provides a detailed analysis of the techniques used, including the use of uncrossable functions and submodularity of the cut function. The paper concludes with a discussion of the implications of these results for network design problems under non-uniform fault models.This paper presents approximation algorithms for network design problems under non-uniform fault models. The Survivable Network Design Problem (SNDP) is a well-studied problem, but its approximability is less understood in more complex models. The paper focuses on three models: flexible graph connectivity, bulk-robust network design, and relative survivable network design. In the flexible graph connectivity model, the edge set is partitioned into safe and unsafe edges. The goal is to design a network that has desired connectivity properties under the assumption that only unsafe edges up to a specific number can fail. The paper provides constant factor approximations for two special cases of this model: the single pair case and the global connectivity case. These results are based on an augmentation framework and decomposing the families of cuts that need to be covered into a small number of uncrossable families. In the bulk-robust model, the goal is to find a min-cost subgraph that remains connected after the failure of a specified number of edges in any scenario. The paper provides poly-logarithmic approximations for this model when the "width" of the instance is fixed. These results are obtained via two algorithmic approaches and have different tradeoffs in terms of the approximation ratio and generality. The paper also discusses the relative survivable network design model, which allows for higher connectivity even when the underlying graph has small cuts. The paper provides poly-logarithmic approximations for this model when the requirements are small. The paper shows that these problems admit poly-logarithmic approximation algorithms when the widths/connectivity requirements are small. The results are obtained via two different algorithmic approaches. The first uses a cost-sharing argument to show a reduction to the Hitting Set problem. The second uses natural LP relaxations and provides additional benefits such as upper bounds on the integrality gaps of the LP relaxations. The paper also extends these results to the group connectivity generalizations of the models. The results are obtained via a novel framework that combines ideas from the augmentation approach and LP relaxations. The paper provides a detailed analysis of the techniques used, including the use of uncrossable functions and submodularity of the cut function. The paper concludes with a discussion of the implications of these results for network design problems under non-uniform fault models.