The notion of Wheeler languages is rooted in the Burrows-Wheeler transform (BWT), one of the most central concepts in data compression and indexing. The BWT has been generalized to finite automata, the so-called Wheeler automata, by Gagie, Manzini, and Sirén. Wheeler languages have subsequently been defined as the class of regular languages for which there exists a Wheeler automaton accepting them. Besides their advantages in data indexing, these Wheeler languages also satisfy many interesting properties from a language theoretic point of view. A characteristic yet unsatisfying feature of Wheeler languages however is that their definition depends on a fixed order of the alphabet. In this paper we introduce the Universally Wheeler languages \(\textsf{UW}\) , i.e., the regular languages that are Wheeler with respect to all orders of a given alphabet. Our first main contribution is to relate \(\textsf{UW}\) to some very well known regular language classes. We first show that the Strictly Locally Testable languages are strictly included in \(\textsf{UW}\) . After noticing that \(\textsf{UW}\) is not closed under taking the complement, we prove that the class of languages for which both the language and its complement are in \(\textsf{UW}\) exactly coincides with those languages that are Definite or Reverse Definite. Secondly, we prove that deciding if a regular language given by a DFA is in \(\textsf{UW}\) can be done in quadratic time. We also show that this is optimal unless the Strong Exponential Time Hypothesis fails.