Despite decades of study, we still do not fully understand why some massive galaxies abruptly switch off their star formation in the early Universe, and what causes their rapid transition to the red sequence. To determine the quenching mechanisms responsible, we require a large sample of galaxies that are caught in the act of transformation. The rare class of post-starburst galaxies (E+A, k+A) provide a rare opportunity to study this transition phase, but currently only limited numbers have been spectroscopically identified at high-redshift (z > 1). Recently, however, a new photometric technique has been developed that can identify post-starburst (PSB) candidates based on the Principal Component Analysis of galaxy SEDs. When applied to the photometric data of the UKIDSS Ultra Deep Survey (UDS), this method has led to the identification of over 900 candidate PSBs at z between 0.5 and 2. In this poster, I will present spectroscopic verification of this selection technique and demonstrate that ~80 per cent of the photometrically-selected PSB candidates show spectral signatures characteristic of this population (arXiv: 1603.08941). I will also present some initial results on the morphological structure of these PSB galaxies, obtained from an isophotal analysis of their CANDELS HST ACS/WFC3 imaging. The resultant light profiles for PSB galaxies show that they are surprisingly compact and spheroidal at high redshift (z > 1), similar to the old passive population. I will discuss what these results can tell us about the potential quenching mechanisms operating in this important transitional population.