The following video shows the paths taken by galaxies and larger structures, within our region of the universe. This cosmic “bulk flow” is based on a huge amount of astrophysical data, analysed in Tully+ 2014 
. These researchers dubbed this supercluster of galaxies Laniakea, which is Hawaiian for “open skies” or “immense heaven”. It is about 500 million light-years across, which is 5000 times the length of our Milky Way galaxy! The incredible image in the still frame below stuck in my mind since I watched the video years ago. Its (human) artist is credited here.
The red dot shows the location of the Milky Way. Now, matter in the universe is distributed fairly evenly (it is “homogeneous” and “isotropic”) on very large scales. However gravity causes it to clump together on smaller scales, into stars, galaxies, clusters of galaxies, and so on. A ball-like shape tends to collapse along a single one of its axes first into a sheet or “pancake”, then along another axis into a line or thread-like “filament”, and finally into a more compact blob, as shown theoretically by Zeldovich 
. In our universe, matter forms a “cosmic web”, which includes filaments with a heavy “node” at the end — a cluster or supercluster. On the other hand, cosmic “voids” are vast regions containing less matter than average. Over time, the matter clumps further, while the voids grow larger and sparser.
The universe is also expanding (which means nothing more than matter moving apart, arguably). For everything discussed here, this expansion has already been subtracted off, so only the “peculiar velocity” remains. In fact Laniakea as a whole is not gravitationally bound. In the distant future it will split into smaller clusters, which will separate as the universe expands. (At least, based on the current understanding of dark energy.) By the way there is no universal agreement on the name Laniakea, nor on its precise boundary.
I remembered this research because I have been wondering about cosmic filaments. (I hoped they might provide a real-world basis for a certain idealised gravitational scenario I have in mind, for some theoretical work. But even if they don’t fulfil this, it is no loss to experience wonder at the beauty in the universe.)
While filaments are vast, they are mostly empty space, hence their gravity is “weak” so Newtonian theory works well. If you model one as cylindrically symmetric, then most of the gravitational force they exert is sideways, onto the filament. However they tend to end in a heavy cluster or supercluster, hence even a galaxy inside the filament will get pulled along its length. The gravitational acceleration of our galaxy and its neighbours (the Local Group) is only about 10-12m/s2 apparently, which is 10 trillion times less than Earth’s surface gravity! However the effect is cumulative, so over vast time scales this is consistent with the ≈600 km/s speed of the Local Group today.