The number of students with Specific Learning Difficulties (SpLDs) taking language proficiency tests is increasing. It is therefore essential that neither the test design nor test implementation procedures create an unfair barrier for these students. This talk will give a comprehensive overview what makes a test fair and valid from the perspective of test takers with SpLDs. The presentation will discuss three main issues in relation to fairness, special arrangements and universal design. First, I will consider how special arrangements may impact on the construct being assessed and to what extent that is acceptable or desirable as far as the meaning and usefulness of any test score outcomes are concerned. Second, given the need for special arrangements for certain test taker groups, the talk will give an overview how accommodations might be differentially beneficial for test takers with SpLDs. I will present recent research findings from our team on how various types of special arrangements such as time-extension and read-aloud affect the performance of students with SpLDs and those without SpLDs. Some of these research findings show that everyone might benefit from certain types of special arrangements, which means that test takers in general may not be able to demonstrate the best of their knowledge under standard test administration conditions. Therefore, the third theme of the talk will focus on universal design, which aims to ensure that the diverse needs of individuals are met flexibly so that language tests become more accessible for everyone including candidates with SpLDs.