This thesis describes research on filtering methods using RandomMatrix Theory (RMT) Models in financial markets. In particular, a novel, stability-based RMT filter is proposed and its potential, for reducing stock portfolio risk, is compared to two well-known alternatives. In terms of performance, the stability-based filter achieved 17.3% overall improvement in risk reduction for equally weighted forecasts, and 49.2% for exponentially weighted. Of the filters investigated, not only did it prove to be the most effective and consistent, for overall risk reduction, but was also shown to reduce the frequency of large risk increases, (which, despite their importance, have attracted little attention in the literature to date). The full frequency distribution of filter effects is studied and a comprehensive test methodology established. Improvements, on previous approaches, include integrated use of bootstrap analysis and out-of-sample testing. RMT filtering was also applied to the foreign exchange market, which contains far fewer assets than a typical stock portfolio. Filters were shown to reduce inherent currency trading risks, despite the small number of assets involved. Once again, our novel filter resulted in the lowest risk for exponentially weighted forecasts, and was most consistent in reducing overall levels, exhibiting also the fewest large risk increases. Finally, and more generally, RMT filter testing and analysis can be used to demonstrate the value of rapid response models, i.e. those reacting quickly to market events. Despite the fact that these utilise very recent data, much information is typically masked by noise. Filtering is shown to be successful in exposing such key underlying features.