1 The glacial geomorphological inversion problem is extremely complex and requires a systematic approach including landscape-level classification based on current glaciological understanding of formative conditions for different glacial landform assemblages. In essence this inversion problem is five-dimensional, i.e. composed of three-dimensional space, time and process components.

2 We recognize that three event or flow types are rquired as a minimum in order to capture real-world complexity. These are the deglacial envelope, event swarms and ice-stream swarms.

3 Meltwater landforms (eskers, meltwater channels, traces of glacial lakes) form a data layer that can and should be used independently of glacial lineations for tracing the retreat pattern.

4 Ice-stream webs also appear to have been extremely important in the former mid-latitude ice sheets. Deciphering of such landscapes involves the same basic techniques as sheet-flow landscapes, but the time-scale for major flow-pattern changes is much shorter than in sheet-flow landscapes.

5 Palaeo-ice streams may provide the best chronological constraints for subglacial events and evolution, because they are the synchronously formed vehicles that allow extramarginal datings on sediments or landforms to be linked to flow traces in the interior of the ice sheet.

6 Relict landscapes, i.e. landscapes lacking a clear glacial imprint or composed of ancient glacial landforms, are important components in formerly glaciated areas. These landscapes offer important insight into former basal conditions, and may preserve direct evidence of ice-sheet configurations and flow-patterns much older than the last glacial maximum.

7 Two examples, from northern Fennoscandia and Keewatin, show that the outlined inversion approach can be applied successfully.

8 The full potential of geomorphological inversion can be realized only when geomorphologists (three-dimensional space) directly collaborate with dating experts (time) and numerical ice-sheet modellers (glaciological processes). Only thereby are all five relevant dimensions of the problem fully addressed.

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