Almost all structures in service are exposed to loads with variable amplitudes, often termed as spectrum loading; many in-service failures occur because this type of loading is not considered properly. In spite of this fact, only a minority of all publications in the fatigue domain are related to variable amplitude loading, and the majority concentrate on constant amplitude loading. Especially for applications in different industrial sectors such as automotive, railway, aircraft, maritime, plant and civil engineering, and renewable energies, various facets of spectrum loading have to be considered in design, and a solid background should be provided for reliable and economic design and safe operation of structures.A series of conferences on Material and Component Performance under Variable Amplitude Loading (VAL) has been initiated on this specific topic starting in 2002 in Tours, France, followed in 2009 in Darmstadt, Germany, and then in 2015 in Prague, Czech Republic, bringing together worldwide experts from science and industry. The fourth of this series (VAL4) was originally scheduled to take place in Darmstadt, Germany, from 30 March to April 1, 2020, in order to address the following topics: load assumptions, modeling of fatigue damage and crack growth, design and analysis methods and tools, reliability concepts, advanced materials and manufacturing, testing, effects on lifetime, numerical assessment, and verification. However, VAL4 unfortunately had to be cancelled at short notice because of Covid-19.In this FFEMS Virtual Special Issue "Variable Amplitude Loading-Fracture Mechanics and Cumulative Damage Modeling," a selected set of extended papers of contributions to VAL4 is presented (available at https:// onlinelibrary.wiley.com/doi/toc/10.1111/(ISSN)1460-2695. Variable-Amplitude-Loading). Another set of the contributions has been published in parallel in the Virtual Special Issue "Variable Amplitude Loading-Load Assumptions and Structural Durability" of the International Journal of Fatigue.The present FFEMS Virtual Special Issue focuses on fracture mechanics and cumulative damage modeling, damage detection, and inspection intervals using frequency domain concepts, elastic-plastic deformation, and thermal load effects.