  Chirality and current-driven dynamics of topologically nontrivial
360$^{\circ}$ domain walls (360DWs) in magnetic heterostructures (MHs) are
systematically investigated. For MHs with normal substrates, the static 360DWs
are N\'{e}el-type with no chirality. While for those with heavy-metal
substrates, the interfacial Dzyaloshinskii-Moriya interaction (iDMI) therein
makes 360DWs prefer specific chirality. Under in-plane driving charge currents,
as the direct result of "full-circle" topology a certain 360DW does not undergo
the "Walker breakdown"-type process like a well-studied 180$^{\circ}$ domain
wall as the current density increases. Alternatively, it keeps a fixed
propagating mode (either steady-flow or precessional-flow, depending on the
effective damping constant of the MH) until it collapses or changes to other
types of solition when the current density becomes too high. Similarly, the
field-like spin-orbit torque (SOT) has no effects on the dynamics of 360DWs,
while the anti-damping SOT has. For both modes, modifications to the mobility
of 360DWs by iDMI and anti-damping SOT are provided.
