The BMW algebras B_n(q,t) are the q-analogues of the Brauer algebras and are in Schur-Weyl duality with quantum groups of types B, C, D. In the semisimple case, they fit in a multiplicity free chain of algebras and are equipped with a remarkable family of commuting elements, called the Jucys-Murphy (JM) elements. In this talk, we will determine the exact parameters q,t with q not a root of unity for which the centers of the BMW algebras are given as a subalgebra of the algebra of symmetric Laurent polynomials in the JM elements, called Wheel Laurent polynomials. As a corollary, we determine when the algebra generated by the JM elements is maximal commutative and, in these cases, give an Okounkov-Vershik-like approach to its finite dimensional representations. If time permits, we will talk about how one can get explicitly defined combinatorial formulas for a complete set of primitive idempotents in B_n(q,t) using this approach.