Structural and non-structural damage reported after recent strong earthquakes promotes a fundamental shift in structural design target from “collapse resistance” to “fast structural function recovery”. A unique class of metal called superelastic shape memory alloy (SMA) has been emerging as a promising solution to enhance the seismic resilience of structures. SMA core damping elements are the basic constituents of many newly-proposed seismic resistant members or devices, and they are directly responsible for the safety, integrity, and economical efficiency of the structures using them. This mini-review paper offers a comprehensive summary of the emerging SMA core damping elements recently developed, covering SMA monofilament wires, fibers, bars, flat plates, U-shaped plates, angles, cables, rings, helical springs, disc springs, and friction springs. These SMA core elements are suitable for various seismic application scenarios, and their efficiency have been verified through either full-scale or proof-of-concept experimental studies. The basic working principles, advantages, and potential shortcomings of these elements are discussed, and future research needs are outlined.