Most algorithms to compute a Gröbner basis are “static”, inasmuch as they require as input both a set of polynomials and a term ordering, and preserve the term ordering throughout the computation.  This talk presents ongoing work on “dynamic” Buchberger algorithms. First described by Sturmfels and Caboara, dynamic algorithms require only a set of polynomials as input, and compute a Gröbner basis with respect to a “discovered” ordering. We describe how one can minimize the time spent identifying potential orderings; which heuristics seem to be good at generating relatively small bases, relatively efficiently; and how we can apply the dynamic approach to non-Buchberger algorithms such as F4 and F5.