In today's hyperconnected world, where every aspect of our lives is intertwined with the Internet, ensuring the reliability, security, and seamless functionality of networks is paramount. Network providers regularly introduce updates to enhance user experience and address emerging challenges, necessitating thorough verification before deployment. Network verification, the process of validating whether a network aligns with specified protocols and meets desired properties and objectives, plays a crucial role in maintaining optimal network performance. Numerous tools, including those employing Satisfiability Modulo Theories (SMT) solvers as their backend, are employed for this purpose. This work delves into the realm of SMT solvers, unraveling their mechanics and exploring their application in the verification of diverse network protocols and properties. We undertake a comprehensive examination of various off-the-shelf SMT solvers, conducting a comparative analysis to evaluate their efficacy in network verification. Through this work, we aim to provide insights into the intricacies of SMT solvers, their role in ensuring network robustness, and a comparative assessment to guide network practitioners and researchers in selecting the most suitable SMT solver for their verification needs.