This paper examines regime switching behaviour and dynamic linkages among currency and equity markets of Eurozone, India, Japan and U.S. using a Markov-switching framework. First, we seek to characterize the market specific and common regime shifts in international stock and currency markets. Second, we aim to study regime-dependent conditional correlations across these markets. We estimate state-dependent models for the financial markets in a univariate Markov-switching Autoregression (MS-AR) as well as a multivariate Markov-switching Vector Autoregression (MS-VAR) framework. The paper utilizes weekly data from July, 1999 to October, 2020 to model the interactions among the markets. Our univariate results identify two-states viz . bull state (bear state) characterized by high returns (low returns) and low volatility (high volatility) for the stock market indices and Euro/USD and INR/USD returns. For the Yen/USD market the bull state corresponds to depreciation accompanied by low volatility. Further, we employ a multivariate formulation to study the regimes across asset classes which provides additional insights into the common states across the markets. Using the MS-VAR model encompassing stocks and currencies, we find a tranquil regime characterized by lower volatility and higher returns and a turbulent regime depicted by higher volatility and lower returns. Contemporaneous correlations among asset market pairs are sharper during the crises. Some of the turbulent periods highlighted in the analysis include the dot-com bubble burst, South American crisis, 9/11, Iraq war, housing bubble burst, global financial crisis, Eurozone debt crisis, Taper Tantrum, Brexit, U.S. Federal Government Shutdown, U.S.-China Trade War and the recent COVID-19 pandemic.