The fabrication and applications of quasicrystals often involve multigrain aggregates. Microstructures and textures of polycrystals can be conveniently studied by orientation mapping. Such studies of quasicrystals have been rare because the widely used electron backscatter diffraction (EBSD) mapping systems do not index patterns from materials with non-crystallographic symmetries. This complication can be circumvented by using a commercial system to detect individual EBSD bands and an in-house software to index the bands and determine the orientations. This approach was applied to decagonal Al–Co–Ni and Al–Co quasicrystals obtained by the melt-spinning technique. The investigated samples showed similar textures and microstructures on the wheel sides of the ribbons. Maps of cross-sections and free sides revealed microstructural differences implying differences in solidification mechanisms. The growth in Al–Co was columnar, whereas ribbons of Al–Co–Ni showed columnar-to-equiaxed transition. The study demonstrates applicability of the conventional orientation mapping based on detection of diffraction reflections to decagonal quasicrystals.