Thinking about the future relies on the use of frameworks of understanding upon which to base different modes of futures thinking. These frameworks are often implicit and thereby not usually subject to being critically examined. The development of a 'generic foresight process' framework has allowed the critical selection of distinct and appropriate frameworks of understanding for use in foresight work and futures research matched to context and scope. As part of this work, a generalised framework for 'layered methodology' has also been developed, in which the 'deepest' level of interpretive inquiry is the 'historical' level, in which the scope---in both space and time---could involve just one society, a number of societies or civilizations, or, on the grandest of all scales, might encompass cosmology and Universal evolution. Thus, by using historical and macrohistorical models, theories and perspectives---of increasing scope and time-frame---we may look for insights about potential futures at a very deep level and thereby undertake profoundly 'deep' futures thinking. Perhaps the grandest model currently available for use in this way is the scenario of Cosmic Evolution, which includes the specific case of how that evolution has played out here on Planet Earth, namely, what has come to be known as 'Big History'. This paper will: introduce the elements of the generic foresight process framework; examine a variety of different types of futures thinking; 'locate' the use of macrohistorical models within the broader foresight thinking process; examine some key aspects of the Big History perspective; and use this perspective to conduct 'macro-prospection'; i.e., to think systematically about the future, informed by Big-Historical thinking. From this will emerge a thumbnail sketch of some of the issues we may need to confront at the civilizational, planetary, and even species level as we navigate our way into the future. It is hoped that the activity of generating such a sketch---as well as demonstrating the processes of thinking that lead to it---will help contribute to the successful navigation by humanity into the rapidly emerging and increasingly dangerous future.