This study examines the effects of unconventional monetary policies (UMPs) by the major central banks, namely the Bank of England (BOE), Bank of Japan (BOJ), European Central Bank (ECB) and the Federal Reserve (Fed), on the international financial markets, taking global spillovers and monetary policy interaction into account. To this end, we applied the Global Vector Autoregressive (GVAR) model to 35 countries/economies and one region for the period from March 2009 to July 2019. In addition, we accommodated the smooth transition to the GVAR to consider possible structural changes in the effects of UMPs and monetary policy interaction. Our results indicate the importance of capturing structural changes, showing the remarkable difference between the beginning and end of the sample. For example, we found clear evidence of monetary policy coordination after the global financial crisis and less evidence of policy interaction in the recent period. Also, our results suggest that generally, the UMPs of the major central banks had stronger effects on both domestic and international bond markets in the earlier period. In contrast, the global equity markets responded more positively to the UMPs in the recent period, although there was no noticeable difference in the responses of domestic equity markets throughout the sample.