This article asserts that current approaches to enhance the accessibility of Web resources fail to provide a solid foundation for the development of a robust and future-proofed framework. In particular, they fail to take advantage of new technologies and technological practices. The article introduces a framework for Web adaptability, which encourages the development of Web-based services that can be resilient to the diversity of uses of such services, the target audience, available resources, technical innovations, organisational policies and relevant definitions of 'accessibility'.The article refers to a series of author-focussed approaches to accessibility through which the authors and others have struggled to find ways to promote accessibility for people with disabilities. These approaches depend upon the resource author's determination of the anticipated users' needs and their provision. Through approaches labelled as 1.0, 2.0 and 3.0, the authors have widened their focus to account for contexts and individual differences in target audiences. Now, the authors want to recognise the role of users in determining their engagement with resources (including services). To distinguish this new approach, the term 'adaptability' has been used to replace 'accessibility'; new definitions of accessibility have been adopted, and the authors have reviewed their previous work to clarify how it is relevant to the new approach.Accessibility 1.0 is here characterised as a technical approach in which authors are told how to construct resources for a broadly defined audience. This is known as universal design. Accessibility 2.0 was introduced to point to the need to account for the context in which resources would be used, to help overcome inadequacies identified in the purely technical approach. Accessibility 3.0 moved the focus on users from a homogenised universal definition to recognition of the idiosyncratic needs and preferences of individuals and to cater for them. All of these approaches placed responsibility within the authoring/publishing domain without recognising the role the user might want to play, or the roles that other users in social networks, or even Web services might play.Adaptability shifts the emphasis and calls for greater freedom for the users to facilitate individual accessibility in the open Web environment.