SummaryAlthough the mechanics of free‐standing rocking cores have been amply investigated and that numerous replaceable energy dissipating devices with recentring capabilities have been proposed, the literature on complete sustainable earthquake resistant structures has not been fully developed. Seismic sustainability (SS) can be achieved if and only if the structure is capable of collapse prevention (CP) and/or post‐earthquake realignment and repairs (PERR). Rigid rocking core moment frame (RRC‐MF) combinations are special earthquake resistant structures that are capable of damage control, elimination of residual effects, CP, and PERR. High strength cables are commonly utilized as rocking core stabilizers, gap opening and closing regulators as well as energy absorbing devices. RRCs are articulated shear walls developed to reduce relative drift and seismic demand on earthquake‐resistant structures (ERSs), prevent plastic collapse, and help realign the system as needed. After discussing sustainable seismic design (SSD), the mechanics of hybrid rocking–stepping cores and self‐centering steel beams are briefly examined. The following innovations are introduced as part of the current article: (1) introduction to global stiffness reduction (GSR), (2) introduction to restoring force adjustment (RFA), (3) the hybrid rigid rocking–stepping core (RRC), (4) tendon‐enhanced replaceable energy dissipating moment connections (REDMCs), and (5) the heat‐generated realignment system.