The rapid advancements in quantum hardware and software have heightened the need for reliable, error-free quantum program development. Unlike classical computing, where decades of research have led to mature debugging techniques, directly applying these methods to quantum software remains challenging due to the fundamental differences rooted in quantum mechanics. Moreover, the inherent complexity of quantum programs makes manual debuggingQuantum debugging impractical, even for small circuits. In this context, this work provides a comprehensive review of existing techniques developed to support quantum program correctness, with a particular focus on assertion-based debuggingAssertion-based debugging approaches. The paper also highlights key research challenges and open issues in this emerging area.