This chapter provides an in-depth examination of Generalized Inverse Bottleneck Optimization Problems (GIBOPs), presenting a unified framework for understanding and solving these complex combinatorial optimization issues. We explore various problem formulations, develop efficient algorithms under different norm constraints, and discuss the computational complexities involved. Practical applications in network optimization and other fields are highlighted, along with a set of open problems that pave the way for future research. It is a significant contribution to the field of (GIBOP), offering both theoretical insights and practical solutions.