Strontium titanate (SrTiO3), famously described by Nobel laureate K. A. M\"uller as the "drosophila of solid-state physics", has been extensively investigated over the last seventy five years for its intricate coupling of structural, electronic, and dielectric properties and continues to serve as a foundational platform for advancing oxide electronics. In its pristine form, SrTiO3 exhibits quantum paraelectric behavior below 35 K and undergoes an antiferrodistortive phase transition near 105 K. This transition generates ferroelastic twin domains separated by a dense network of domain walls, which function as nanoscale structural defects with far-reaching consequences. While the static influence of ferroelastic domain walls on carrier transport in electron-doped SrTiO3 is well established, recent experimental results show that the emergence of polarity at these walls, combined with strain fields and inherent quantum fluctuations, induces correlated dynamical phenomena such as glass-like relaxations of electrons and memory effects. In this review, we highlight these recent advances, focusing on the subtle interplay between the emergence of nanoscale polar order, quantum fluctuations, and long-range strain fields. We propose that understanding charge carrier dynamics in the background of these complex ferroelastic domain wall landscapes offers a new paradigm for exploring electronic transport in the presence of local polar order and quantum fluctuations, with broad implications for correlated oxides.