Quantifying morphological evolution from low to high redshifts

Establishing the morphological history of ordinary galaxies was one of the original goals for the Hubble Space Telescope, and remarkable progress toward achieving this this goal has been made. How much of this progress has been at the expense of the Hubble sequence? As we probe further out in redshift space, it seems time to re-examine the underlying significance of Hubble's tuning fork in light of the the spectacular and often bizarre morphological characteristics of high redshift galaxies. The aim of this review is to build a morphological bridge between high-redshift and low-redshift galaxy populations, by using quantitative morphological measures to determine the maximum redshift for which the Hubble sequence provides a meaningful description of the galaxy population. I will outline the various techniques used to quantify high-redshift galaxy morphology, highlight the aspects of the Hubble sequence being probed by these techniques, and indicate what is getting left behind. I will argue that at higher redshifts new techniques (and new ideas) that place less emphasis on classical morphology and more emphasis on the link between morphology and resolved stellar populations are needed in order to probe the evolutionary history of high-redshift galaxies.