In this paper, we use the unstructured grid model SCHISM to simulate the thermohydrodynamics in a chain of baroclinic, interconnected basins. The model shows a good skill in simulating the horizontal circulation and vertical profiles of temperature, salinity, and currents. The magnitude and phases of the seasonal changes of circulation are consistent with earlier observations. Among the mesoscale and subbasin-scale circulation features that are realistically simulated are the anticyclonic coastal eddies, the Sebastopol and Batumi eddies, the Marmara Sea outflow around the southern coast of the Limnos Island, and the pathway of the cold water originating from the shelf. The superiority of the simulations compared to earlier numerical studies is demonstrated with the example of model capabilities to resolve the strait dynamics, gravity currents originating from the straits, high-salinity bottom layer on the shallow shelf, as well as the multiple intrusions from the Bosporus Strait down to 700 m depth. The warm temperature intrusions from the strait produce the warm water mass in the intermediate layers of the Black Sea. One novel result is that the seasonal intensification of circulation affects the interbasin exchange, thus allowing us to formulate the concept of circulation-controlled interbasin exchange. To the best of our knowledge, the present numerical simulations, for the first time, suggest that the sea level in the interior part of the Black Sea can be lower than the sea level in the Marmara Sea and even in some parts of the Aegean Sea. The comparison with observations shows that the timings and magnitude of exchange flows are also realistically simulated, along with the blocking events. The short-term variability of the strait transports is largely controlled by the anomalies of wind. The simulations demonstrate the crucial role of the narrow and shallow strait of Bosporus in separating the two pairs of basins: Aegean-Marmara Seas from one side and Azov-Black Seas from the other side. The straits of Kerch and Dardanelles provide sufficient interbasin connectivity that prevents large phase lags of the sea levels in the neighboring basins. The two-layer flows in the three straits considered here show different dependencies upon the net transport, and the spatial variability of this dependence is also quite pronounced. We show that the blocking of the surface flow can occur at different net transports, thus casting doubt on a previous approach of using simple relationships to prescribe (steady) outflow and inflow. Specific attention is paid to the role of synoptic atmospheric forcing for the basin-wide circulation and redistribution of mass in the Black Sea. An important controlling process is the propagation of coastal waves. One major conclusion from this research is that modeling the individual basins separately could result in large inaccuracies because of the critical importance of the cascading character of these interconnected basins.