This thesis focuses on how portfolio optimisation can be carried out under different types of uncertainty, which we often measure through the use of filters. Chapter 1 motivates the problem, gives an overview of the thesis and covers some necessary background material. Chapter 2 deals with uncertainty in the covariance matrix and how by identifying different regimes we can solve optimisation problems of interest to practitioners. Chapter 3 focuses on the uncertainty over tail events and how we can not only extract relevant information by filtering the data but also how we can use that information to construct a portfolio optimisation problem that acts on it. In Chapter 4 we address the lack of tractability for general relative robust portfolio optimisation problems and how one can overcome this so as to make it a viable tool. Chapter 5 considers the problem of uncertainty in the filter itself and how this uncertainty can be fully incorporated in the portfolio optimisation problem. Finally in Chapter 6 we conclude and propose topics for future research.