  With its central role in conventional BCS superconductivity, electron-phonon
coupling has appeared to play a more subtle role in the phase diagram of the
high temperature superconducting cuprates. The added complexity of the cuprates
with potentially numerous competing phases including charge, spin, orbital, and
lattice ordering, makes teasing out any unique phenomena challenging. In this
review, we present our work using angle resolved photoemission spectroscopy
(ARPES) to explore the role of the lattice and its effect on the valence band
electronic structure in the cuprates. We provide an introduction to the ARPES
technique and its unique ability to the probe the effect of bosonic
renormalization (or "kink") on the near-E$_F$ band structure. Our survey begins
with the establishment of the ubiquitous nodal cuprate kink leading to the way
isotope substitution has shed a critical new perspective on the role and
strength of electron-phonon coupling. We continue with recently published work
on the connection between the phonon dispersion as seen with inelastic x-ray
scattering (IXS) and the location of the kink as observed by ARPES near the
nodal point. Finally, we present very recent and ongoing ARPES work examining
how induced strain through chemical pressure provides a potentially promising
avenue for understanding the broader role of the lattice to the superconducting
phase and larger cuprate phase diagram.
