[Picture credit: Suvendra Dutta]
The closest void in our galactic neighborhood is called the 'local void'. It is empty except for a lonely dwarf galaxy whose velocity indicates it's trying to move out of the void. That behavior is what one would expect to happen to underdense regions during structure formation. According to estimates following from ΛCDM simulations one would also expect there to be about ten dwarf galaxies in this void . So where are they? Why is the void so empty?
However, what is usually computed in structure formation simulations is not the distribution of visible matter but that of dark matter, and our usual matter follows the dark matter's structures. Thus, what we actually know is that there are too many dark matter dwarf haloes in the simulations as compared to data. It might thus be the problem is not one with the void, but that dark matter haloes just failed to form galaxies. ΛCDM also predicts too many dwarf dark matter haloes as compared with the observed dwarf galaxies . The solution to that puzzle might thus be on the cosmological side - in case there's something about structure formation we haven't yet got quite right - or on the astrophysical side - in case there's something about galaxy formation we haven't appropriately incorporated.
Tinker and Conroy  recently extrapolated the halo occupation distribution (the relation between dark matter halos and galaxies) into regimes in which observational data is lacking in order to model the distribution of dwarf galaxies. In doing so, they claim to be able to model the emptiness of voids, which would mean the explanation is on the astrophysical side. Tikhonov and Klypin  however point out that to explain the void structures, small haloes with circular velocity Vc > 20 km/s should not host galaxies, which however they do: they include a table with properties of observed isolated dwarf galaxies with circular velocities of about 20 km/s. Tikhonov and Klypin conclude
"We would like to emphasize that the disagreement with the theory is staggering. The observed spectrum of void sizes disagrees at many sigma level from the theoretical void spectrum if haloes with Vc > 20 km/s host galaxies brighter than MB = −12."
There is no bottomline to this post, I'm just trying to summarize some stuff I recently read. I'm still not entirely sure what to make out of the void problem, any comments are welcome.
 A. Tikhonov and A. Klypin "The emptiness of voids: yet another over-abundance problem for the LCDM model" arXiv:0807.0924v1 [astro-ph]
 P. J. E. Peebles, "Galaxies as a cosmological test" arXiv:0712.2757v1 [astro-ph]
 Jeremy L. Tinker and Charlie Conroy "The Void Phenomenon Explained" arXiv:0804.2475v2 [astro-ph]
 Strigari at al "Redefining the Missing Satellites Problem" arXiv:0704.1817v2 [astro-ph]