This book proposes a simple framework based on variance decompositions from approximating vector autoregressions to define, measure and monitor network connectedness, and applies its methods in financial and macroeconomic contexts. In financial markets, for example, there is focus on connections among different assets, asset classes, or portfolios, as well as the stocks of individual institutions, and the objects connected are typically returns or return volatilities. Similarly, in macroeconomics the book discusses cross-country real output connections (that is, the global business cycle). On the financial side, the book shows that stock markets played a critical role in spreading volatility shocks from the U.S. to other countries during the Great Recession. Furthermore, although return connectedness across stock markets increased gradually, volatility connectedness jumped quickly. On the macroeconomic side, the book shows that global business cycle connectedness is economically significant and time varying, that the U.S. has disproportionately high net connectedness to others, and that pair-wise net connectedness is inversely correlated with bilateral trade surplus.