Heavy (bottom and charm) quarks are ideal probes of the nonperturbative dynamics of confinement, since heavy quarks effectively serve as static color sources during the entire hadronization cascade. In this talk, I present the new study of transverse momentum- dependent (TMD) fragmentation functions (FFs) for heavy quarks, demonstrate their factorization in terms of novel nonperturbative matrix elements in heavy-quark effective theory (HQET), and prove new TMD sum rules that arise from heavy-quark spin symmetry. I also include the next-to-leading order calculation of the unpolarized heavy-quark TMD FF, which is important for other collider observables such as the energy-energy correlator in the back-to-back limit. I further present the calculation of all TMD parton distribution functions for the production of heavy quarks from polarized gluons within the nucleon, and use our results to demonstrate the potential of the future EIC to resolve TMD heavy-quark fragmentation in semi-inclusive DIS, complementing the planned EIC program to use heavy quarks as probes of gluon distributions.