The large ice sheets on Earth respond to changes in the global climate. Ice mass loss increases with rising global mean temperature and thus is a major contributor to sea-level rise. In order to reduce the uncertainty to predict the contributions to sea-level rise of ice sheets, it is crucial to study how the ice sheets‘ fast-flowing drainage pathways (so-called ice streams) have evolved over the last thousand to millions of years. In this thesis, a contribution to the understanding of the flow characteristics of large ice streams in Greenland and Antarctica is performed by an analysis of (ice-penetrating) radar reflections within the ice column and at the ice base. My focus lies on the question how these data can be used to obtain information about present and paleo ice flow regimes. I concentrate on radar data acquired in Northeast Greenland in the upstream regions of the North East Greenland Ice Stream (NEGIS) and in the upstream catchment of the Nioghalvfjerdsbrae (79°N Glacier) as well as on data recorded at the onset of the Jutulstraumen Glacier in Antarctica. In my studies, I show that the NEGIS in its present form is a relatively young feature and that its geometry and flow characteristics are intertwined with the subglacial topography. I also found indications for a re-organization of ice stream activity in the NEGIS catchment during the Holocene. This suggests that ice streams are probably are less persistent than previously thought and adapt in their entire length to the changing geometry of the ice sheet on short time scales. In Antarctica, I investigate past ice flow patterns over a period of millions of years, as in the example of the Jutulstraumen Glacier basin in Antarctica. Many of the glacial and fluvial landscapes, which developed since the glaciation of Antarctica, have been mostly preserved under the contemporary thick ice sheet, and some even serve as basins for active subglacial lakes today.