This thesis consists of four chapters that focus on the development of new statistical frameworks or tests of financial market crisis and contagion. A new test for financial market contagion based on changes in the fourth order co-moments is proposed in chapter 2 to identify the propagation mechanism of shocks across international financial markets. The proposed approach captures changes in various aspects of the asset return relationships such as cross-market mean and skewness (co-kurtosis) as well as cross-market volatilities (co-volatility). In an empirical application involving the global financial crisis of 2008-09, the results show that significant contagion effects are widespread from the US banking sector to global equity markets and banking sectors through either the co-kurtosis or the co-volatility channel. Chapter 3 analyses nine financial crises from Asia in 1997-98 to the recent European debt crisis of 2010-13 to answer the question of whether the great recession is different to other crises in terms of a range of hypotheses regarding contagion transmission. This chapter examines financial contagion with a focus on the correlation and co-skewness change tests, and the proposed co-volatility change test in chapter 2 to capture changes in the various aspects of the asset return relationships. The empirical results indicate that the great recession and European debt crisis are truly global financial crises. Linkages through financial channels are more likely to result in crisis transmission than through trade, and crises beginning emerging markets transmit unexpectedly, particularly to developed markets. Chapter 4 introduces a new class of multiple-channel tests of financial market contagion in which the transmission channels of financial market crises are identified jointly through the correlation, co-skewness and co-kurtosis of the distribution of returns. The proposed tests yield the correct size in small samples which is typical of crisis periods. Regarding the power of the tests, the multiple-channel tests display the second highest power following the single-channel tests if the data generating process for an experiment contains the transmission channel of contagion consistent with the single-channel test. In an empirical application involving the three financial crises of 2007-12, the results show that the joint tests identify various combinations of transmission channels. Chapter 5 introduces new framework for testing for crisis and contagion using a regime switching skew-normal model (RSSN model). This new approach provides a more general framework for developing five types of crisis and contagion channels simultaneously. Measuring financial contagion within the RSSN model can solve several econometric problems. These are i) market dependence is fully captured by simultaneously considering both second and third order co-moments of asset returns; ii) transmission channels are simultaneously examined; iii) crisis and contagion are distinguished and individually modelled; iv) the market that a crisis originates is endogenous; and v) the timing of a crisis is endogenous. By applying the proposed model to equity markets during the great recession using Bayesian model comparison techniques, the results generally show that crisis and contagion are pervasive across Europe and the US through the second and third moment channels during the great recession.