Spatial metaphors are ubiquitous in political communication. One talks about political positions, political landscapes, and about the distances between opinions or positions of political actors. Thus, it is natural to consider spatial representations of political opinions: Political spaces. The main level of political discourse, that can be observed directly, is the level of political issues. We consider anything on which a political decision can be made as a political issue. The issue space is spanned by the possible attitudes on issues that are the object of political decisions in all fields of politics. This space itself has a multi-level structure, because these issues can be considered at different levels of aggregation. For a single actor, such as a politician, a political party, or a voter the attitude towards these issues is represented as a point (or region) in this issue space. If a population of such actors is considered, the attitudes on the single issues will be normally not statistically independent. Due to these correlations, the attitudes of the population might be approximately represented in a low dimensional space, called "political spaces". In the present contribution, we will present examples for the inference of such political spaces from Twitter data and we will compare it with simulations of a multi-issue opinion dynamics model. The model is based on three different ingredients: (1) interacting agents align their views regarding the significance of different argumentative domains; (2) belief structures - different (partially overlapping) sets of these domains are associated with different political issues and an agent’s attitude is a function of the importance assigned to the argument domains and their evaluative relevance for the issues - and (3) agents preferentially interact with other agents that hold similar attitudes. We show under which conditions these combined processes give rise to polarization and discuss the role of correlations of attitudes towards multiple political issues in this context.