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This thesis carries out a series of empirical investigations into the nature and evolutionary process of asset bubbles in global stock markets. It also provides insight into the issue of market predictability with the consideration of price bubbles in the US, and how those results might inspire policymakers to prevent future bubbles. We start by reviewing the rational bubble theories which are used for modelling bubble process and discuss the rationale of the relevant testing methods for discovering bubbles. Overall, three main testing procedures are selected in Chapter 3 with the purpose of concluding whether bubbles exist in the global stock markets. Eventually, we confirm the presence of bubbles globally, and provide clear dates for each bubble's origination and collapse. The bubble dates obtained provide a timeline for stock market exuberance, and their overlapping periods suggest that bubbles can migrate between countries. However, there has been very little research on this latter issue. Therefore, in Chapter 4 we undertake a large-scale empirical analysis to investigate the bubble transmission mechanism. Our vector autoregressive (VAR) and volatility results confirm that for some countries a contagion effect exists, leading to bubble migration between countries. Finally, in Chapter 5, we are particularly interested in whether empirical results on the predictability of stock market data by the dividend-price ratio is affected by the presence of a bubble, and by borrowing Campbell-Shiller's model but adding selected monetary variables, we further assess the forecasting performance of common monetary policy indictors in predicting the movement of price-dividend ratios in both bubble and non-bubble periods.