The phonon-mediated attractive interaction between carriers leads to the Cooper pair formation in conventional superconductors. Despite decades of research, the glue holding Cooper pairs in high-temperature superconducting cuprates is still controversial, and the same is true for the relative involvement of structural and electronic degrees of freedom. Ultrafast electron crystallography (UEC) offers, through observation of spatiotemporally resolved diffraction, the means for determining structural dynamics and the possible role of electron-lattice interaction. A polarized femtosecond (fs) laser pulse excites the charge carriers, which relax through electron-electron and electron-phonon couplings, and the consequential structural distortion is followed diffracting fs electron pulses. In this paper, the recent findings obtained on cuprates are summarized. In particular, we discuss the strength and symmetry of the directional electron-phonon coupling in Bi2Sr2CaCu2O8+delta (BSCCO), as well as the c-axis structural instability induced by near-infrared pulses in La2CuO4 (LCO). The theoretical implications of these results are discussed with focus on the possibility of charge stripes being significant in accounting for the polarization anisotropy of BSCCO, and cohesion energy (Madelung) calculations being descriptive of the c-axis instability in LCO.