  In this paper, we review some of the work our group has done in the past few
years to obtain the electron self-energy of high temperature superconductors by
analysis of angle-resolved photoemission data. We focus on three examples which
have revealed: (1) a d-wave superconducting gap, (2) a collective mode in the
superconducting state, and (3) pairing correlations in the pseudogap phase. In
each case, although a novel result is obtained which captures the essense of
the data, the conventional physics used leads to an incomplete picture. This
indicates that new physics needs to be developed to obtain a proper
understanding of these materials.
