We cannot see through the disk of the Milky Way, so how can we tell that there are not any close galaxies just on the other side of it?
You ask a good question! In fact, the most recent galaxy in the Local Group that was discovered is the Sagittarius Dwarf ( Note: scroll to the end for an update!) in the late 1990s, a tiny galaxy that is very close to the Milky Way but hidden behind it from our vantage point on Earth.
There are a few ways that astronomers deduce the presence of a small galaxy right behind the Milky Way, and they all involve looking at other wavelengths than in the optical for the reason you state: visible light doesn't get through to us from the other side of the Milky Way because it gets absorbed by the dust in the disk. However, this isn't as big a problem if you look at light at longer wavelengths which our eyes can't see but which we can detect with specially designed telescopes. In fact, the longer the wavelength of the light the less impeded you are by the dust in the Milky Way, and at radio wavelengths there is no obscuration from the Milky Way at all! So to detect galaxies on the other side of the Milky Way's disk, the first step is to use a radio telescope to detect gas whose motion is different from the Milky Way's. This doesn't work if the galaxy is too close to the Milky Way, though, because then its motion gets mixed up with the motion of the gas in our own galaxy, and it becomes difficult to tell them apart (that's why nobody saw the Sagittarius Dwarf with radio telescopes at first). Another approach is to try and detect the small galaxy's stars in the infrared (longer wavelengths than what our eyes can see but shorter than radio waves). There is some obscuration of dust at these wavelengths to worry about, but with a sensitive telescope it still may be possible to find stars in another nearby galaxy that lies behind the disk of our own.
There still may be galaxies smaller and closer than the Sagittarius Dwarf lurking just behind the Milky Way, that we haven't yet seen. Detecting them is a challenge for future, super-sensitive radio and infrared telescopes!
Update: In a press release on November 4th, 2003, astronomers announced that they have found a new galaxy lurking behind the Milky Way's disk, even closer than the Saggitarius Dwarf: Canis Major. We truly are still finding our closest extragalactic neighbors!
This page was last updated June 28, 2015.