An understanding of the nature of sedimentation at ice-stream lateral margins is important in reconstructing the dynamics of former ice sheets and modelling the mechanisms by which sediment is transported beneath contemporary ice streams. Theories of the formation of ice-stream lateral moraines (ISLMs) have hitherto been based on a relatively limited number of terrestrial and marine examples. Here, an inventory of ISLMs is compiled from available studies, together with independent analysis of seismic-reflection and bathymetric datasets. The locations and dimensions of 70 ISLMs, alongside a synthesis of their key architectural and geomorphic characteristics, are presented. Two different types of ISLMs are identified. Type 1 ISLMs are up to 3.5 km wide and 60 m thick. They maintain a constant width, thickness and cross-sectional shape along their length. Type 1 ISLMs are interpreted and referred to as ice-stream $lateral\; shear-moraines$ that form subglacially in the shear zone between ice streams and slower-flowing regions of an ice sheet. In contrast, Type 2 ISLMs are up to 50 km wide and 300 m thick. They are only identified close to the shelf break in the marine environment. Type 2 ISLMs exhibit an increase in width and thickness along their length and their distal slopes become steeper in a seaward direction. They contain internal dipping reflections that indicate sediment progradation away from the former ice stream. Type 2 ISLMs are interpreted and referred to as ice-stream $lateral\; marginal-moraines$ that were formed at the lateral boundary between ice streams and seafloor terrain that was free of grounded ice. We suggest that, using bathymetric images and acoustic profiles, it is possible to differentiate between ice-stream lateral shear-moraines and lateral marginal-moraines in the geological record. This distinction is important for understanding the mechanisms of sediment transfer beneath ice streams and for making inferences about the conditions that existed beyond the lateral ice-stream margin at the time of lateral-moraine formation: slow-moving ice beyond lateral shear-moraines, and ocean water rather than ice beyond lateral marginal-moraines.