We review some aspects of the spectral theory of the critically coupled Almost Mathieu Operator connected with the structure of the famous associated "Hofstadter's Butterfly." We present a new result (joint with Mira Shamis) establishing that for a topologically generic set of irrational frequencies, the Hausdorff dimension of the spectrum of the critical Almost Mathieu Operator is zero. This result is based a new approach which combines certain inductive WKB-type estimates with Green function techniques and provides more detailed information than what has been previously achieved using more elaborate semiclassical approaches.