We study a class of optimisation problems called minimaximal and maximinimal optimisation problems. In this thesis, we present the first unifying framework for formulating minimaximal and maximinimal optimisation problems, based on a particular partial order concept. To accompany this framework, we define a variety of partial orders, an important example being the partial order of set inclusion. By considering various source optimisation problems from the literature, and partial orders from our collection, we use our framework to obtain a range of minimaximal and maximinimal optimisation problems. We study these individual examples mainly from the point of view of algorithmic complexity.