Matheuristics (MA) combine Mathematical Programming (MP) techniques with Metaheuristics (MH). The goal is to benefit from the precision of MP solvers while leveraging heuristics for efficiency and scalability in solving complex optimization problems. A number of empirical analyses have attempted to understand the performance of MAs for real-world applications such as vehicle routing problems. The goal of this project is to present performance guarantees and insights on problem classes where MAs are effective, through a series of theoretical and empirical analyses. This will lead to further insights into how to apply and design MAs for real-world problems.