Vaughan Jones showed how to associate links in the $3$-sphere to elements of Thompson’s group $F$ and proved that $F$ gives rise to all link types. This talk will introduce Jones’s construction and discuss two recent extensions– the first is a method of building annular links from Thompson’s group $T$, which contains $F$ as a subgroup, and the second is a method of building $(n,n)$-tangles, which give rise to an action of $F$ on Khovanov’s chain complexes. This talk includes joint work with Slava Kruskhal and Yangxiao Luo.