Financial risk management is a dynamic area where new regulation (at international and European levels) will necessitate new approaches.
One theoretical debate is about top-down versus bottom-up models, where the advantages of top-down models (e.g. data availability and ease of estimation) are said to be outweighed by disadvantages such as lacking diagnosis of risk problems, backward looking perspective and lack of incorporating risk mitigation techniques. On the other hand, when deploying bottom-up models (both process approaches and actuarial methods) it is more difficult to aggregate data and provide clear estimates for capital requirements.
Another debate both in the literature and in practice is about Value-at-Risk (VaR) models. Despite their limitations (e.g. regarding extreme values which in financial markets can be heavily tailed), they are still widely used in practice and have become a standard measure for risk management.
I think you need to better define your question. It is very broad, you'll have a world of research areas as simulation, VaR, Bayesian models, standard deviation, CAPM, etc. .. each has its area of these classics.
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