The article combines theoretical and applied aspects of the multiaxial fatigue problem. It presents a brief overview of modern theories and hypotheses, as well as examples of methods, for quantitatively assessing fatigue damage in metallic structures under multiaxial loading. The necessity of conductingthis analysis arises, firstly, from the importance and prevalence of the issue of multiaxial cyclic loading, and secondly, from the extensive number of attempts to address it. The analysis includes characteristics of classical approaches, contemporary models of multiaxial-fatigue damage, and examples of normative documents and methodologies, which have found broad practical application. The aim is to synthesize information on methods for determining damage accumulation under multiaxial loading to identify their potential for further development and application in ensuring the strength and durability of aerospace structural elements. As shown, existing methods for assessing accumulated fatigue damage and predicting durability under multiaxial cyclic loading can be divided into two groups: those ones effective for proportional loading and those ones effective for more complex, non-proportional loading, including in-phase and out-of-phase conditions. Although methods developed for non-proportional loading, particularly based on the critical-plane concept, take into account the geometry of the localized damage plane, they do not consider the crystallographic slip direction on the critical planes. Accounting for rolling texture, as shown while considering aviation aluminium alloy 2024 T3, can bring the Huber–Mises approach for multiaxial loading closer to the real processes occurring in structural materials at the microscale level.