  We use the theory of $\textbf{U}_q$-tilting modules to construct cellular
bases for centralizer algebras. Our methods are quite general and work for any
quantum group $\textbf{U}_q$ attached to a Cartan matrix and include the
non-semisimple cases for $q$ being a root of unity and ground fields of
positive characteristic. Our approach also generalizes to certain categories
containing infinite-dimensional modules. As applications, we give a new
semisimplicty criterion for centralizer algebras, and recover the cellularity
of several known algebras (with partially new cellular bases) which all fit
into our general setup.
