Stellar streams form as smaller gravitationally bound collections of stars are tidally torn apart by a more massive galaxy. In the coming decade, thousands of stellar streams will be observed in the halos of external galaxies. But what fundamental discoveries will we make about dark matter from these streams? In this talk, I discuss dark matter science with stellar streams in external galaxies from both accreted dwarf galaxies and from globular clusters. I first focus on dwarf streams and present new models of the Centaurus A (Cen~A) dwarf companion Dwarf 3 (Dw3) and Dw3's associated stellar stream, to find out what can be learned about the Cen~A dark-matter halo. With a novel external galaxy stream-fitting technique, we find that there are many viable stream models that fit the data well, with reasonable parameters, provided that Cen~A has a halo mass larger than M_200 > 5 x 10^12 Msun. We also find that just one radial velocity measurement breaks degeneracies between stream morphology and dark matter halo mass. In the second part of the talk, I discuss stellar streams from globular clusters (GCs). Due to their low velocity dispersions, these streams are sensitive to gravitational interactions with low-mass dark matter subhalos. In the Milky Way, we know of a handful of stellar streams with noticeable under-densities, however, the Galactic bar, molecular clouds, and spiral arms can also lead to similar signatures in the streams. If we can instead find GC streams in external galaxies without these baryonic perturbers, gaps in such streams could be easier to decipher and serve as a test of LCDM. I present the Hough Stream Spotter (HSS) code which can rapidly and systematically search for linear structures in external galaxies. The HSS combined with the Roman Space Telescope (Roman) will find 100s of thin GC streams in M31 and around galaxies that do not have bars and spiral arms. I conclude that upcoming statistical samples of dwarf and GC streams will be crucial for mapping dark matter in the Universe.