Abstract : Through the recent emergence of joint resource and network virtualization, dynamic composition and provisioning of time-limited and isolated virtual infrastructures is now possible. One other benefit of infrastructure virtualization is the capability of transparent reliability provisioning (reliability becomes a service provided by the infrastructure). In this context, we discuss the motivations and gains of introducing customizable reliability of virtual infrastructures when executing large-scale distributed applications, and present a framework to specify, allocate and deploy virtualized infrastructure with reliability capabilities. An approach to efficiently specify and control the reliability at runtime is proposed. We illustrate these ideas by analyzing the introduction of reliability at the virtual-infrastructure level on a real application. Experimental results, obtained with an actual medical-imaging application running in virtual infrastructures provisioned in the experimental large-scale Grid'5000 platform, show the benefits of the virtualization of reliability.