Twin pregnancies are at increased risk of morbidity and mortality compared to singletons. Among all twins, monochorionic pregnancies are at higher risk of specific and non-specific complications compared to dichorionic pregnancies. Therefore, it is of great importance to properly counsel future parents with monochorionic pregnancies regarding the risks of adverse outcomes and the modalities of monitoring and intervention of the potential complications. Conditions related to the monochorionicity include twin-to-twin transfusion syndrome (TTTS), twin reversed arterial perfusion sequence (TRAP), and twin anemia polycythemia syndrome (TAPS); other complications include selective fetal growth restriction (sFGR) and congenital anomalies. This review aims to summarize the information available in the current literature regarding the complications in monochorionic diamniotic twin pregnancies, including outcomes and guideline recommendations about the clinical surveillance, management, and timing of interventions of these conditions that should be included in counselling in routine clinical practice.