The paper involves reviewing researches, which consider crystallographic aspects of fatigue damage in both metallic polycrystals and single crystals. The primary aim of this work is to substantiate the necessity and feasibility of considering both material texture in polycrystals and the crystallographic orientation of single crystals during the assessment of equivalent stresses under multiaxial loading. Additionally, the study aims to assess quantitatively the accumulated fatigue damage. The tasks undertaken include as follow: analysing contemporary research investigating cases, where surface deformation relief in metals serves as an indicator of accumulated fatigue damage, examining crystallography; studying the surface relief components, and estimating how the texture of constructional metals influences the formation of deformation relief and corresponding fatigue damage. The study provides evidence for the activation of additional slip systems during biaxial loading. It is noted that the Huber–Mises method for assessing equivalent stresses during biaxial loading does not account for anisotropy in constructional materials, such as aluminium alloys commonly used in aviation. Methodologically, the paper considers mechanical tests, light microscopy, x-ray analysis. The main result of the study is the substantiation of the need to consider metals’ crystallographic anisotropy, when calculating equivalent stresses under multiaxial loading. The review of research indicates that the fatigue-damage accumulation and the evolution of surface deformation relief are related closely to the crystallographic orientation of single crystals and crystallites in textured polycrystal materials. Recognizing these crystallographic aspects is essential for thorough estimating accumulated fatigue damage. It demonstrates the necessity and feasibility of considering crystallographic aspects in the development of methods for estimating accumulated fatigue damage. The effect of both the crystallographic orientation of single crystals and the texture of polycrystalline material is pronounced under the uniaxial and biaxial loadings.