So as foreground stars move in front of background stars - for example a star in the Milky Way disk moves in front of a star in the bulge - it can occasionally amplify the bulge star by a large amount. However, since the alignment has to be very precise to get a large amplification, the bulge star will not be amplified for a long time, before the disk star moves away from the ideal lensing alignment.
Because the alignment has to be so good, you need to look at millions of stars to have a chance of seeing significant amplification. So people observed millions of stars toward the LMC and toward the bulge, to find stars that brightened by a lot over a few days. This phenomena is called micro-lensing (because the deflection angle is so small, ).
There is one crucial aspect of lensing that we haven't paid attention
to yet: the deflection and amplification is independent of the
wavelength of the light, as you can see from Eq. (12.3).
This is important if you want to detect micro-lensing, because the
brightness of many stars varies anyway, because they are variable
stars. But in general, the change in brightness for a variable star
depends on the colour you observe it in. But the change in brightness
due to micro-lensing is colour independent. This makes it possible to
distinguish variable stars from lensed stars. In addition, the light
curve - luminosity as function of time - is very easily computed in
terms of 
and the relative velocity of L and S. Combined, it allows
one to confidently detect micro-lensing, and distinguish it from the
case where the star is intrinsically
varying. Figure 12.5 shows an example of micro-lensing
of a star in the LMC, which brightens considerably around day 420,
equally much in the blue as in the red.
Although we so far only considered lensing by stars, in fact any
massive object will produce lensing. This has been exploited by the
MACHO collaboration12.3 to
constrain the nature of the dark matter in the halo of the Milky
Way. Indeed, suppose dark matter consisted of some type of massive
objects, like black holes, or Jupiter-like objects, or some type of
MAssive Compact Halo Object in general. Since
we know that the outer parts of the Milky Way halo is dominated by dark
matter, there should be many such objects between the Sun and the
LMC. If they exist, then we can detect them by their lensing signal.
To detect such MACHO's, the collaboration imaged millions of stars in the
LMC for four years, and indeed found several lensing events like the
one pictured in Fig.12.5. However, it is now believed
that in each case, the lens is actually a normal star in the LMC, and
not some exotic kind of matter. As a consequence, this experiment has
now ruled-out a wide range of dark matter candidates. If the dark
matter is some type of elementary particle, it will not lens LMC stars
(well, it will, but
!), so that is still an option.
The future of micro-lensing is very bright. Suppose for example that the lens is a binary star - then the light curve of the lensed object may be much more complicated, as the source may be lensed by each component of the binary in turn. Such events have already been detected toward the bulge. This is also a very promising way for detecting planets around distant stars, and planned satellite missions will undoubtedly detect planets in this way.