Grey Line
Propagation along the grey line (the line along which dawn / dusk occurs) can produce exceedingly good results with stations from the other side of the globe being audible at the same strengths as many local stations.  
This propagation mode may only be short lived and it will be very selective in terms of relative location.  It is also best during spring and autumn.  
This is of primary benefit in the 15 and 10 meter bands (per FCC exam questions).   Of course it gets more complicated.
Methodology:   The extra class license exam generalizes the "cause of grey-line propagation" as "at twilight and sunrise, D-layer obsorption is low while E-layer and F-layer propagation remains high".  
More specifically, the D layer, which absorbs HF signals, disappears rapidly on the sunset side of the grey line, and it has not yet built upon the sunrise side.  
During the day, solar radiation collides with the molecules in our ionosphere, ripping off electrons.  
These electrons are called "free electrons" because they are not attached to an atom or molecule.  
All of these free electrons cause the density of the ionosphere to increase.  
The more dense the ionosphere, the higher the frequency that is reflected back to earth.  
The electron density is what determines the maximum usable frequency (MUF), and the action of solar radiation separating electrons from the molecules is called ionization.  
During the day, solar radiation causes ionization to stratify, that is, to form distinct layers.  
The ionospheric layer closest to the earth is called the D-Layer.  
It does not reflect signals generally, but does absorb some of the energy, and hence the D-Layer is often called the "absorption layer".  
Higher up in our ionosphere, we find the E- and F-Layers.  
These layers do reflect the signals back to earth if they are below the MUF, and is exactly what causes "skip propagation".  
So during the day, the sun is ionizing the D, E and F layers (there are actually two F layers, called F1 and F2).  
Your 10 meter signal must travel through the D-Layer, getting attenuated, then bounces back from the E or F layer hopefully to some DX spot, passing through the D-Layer for more absorption again.  
But since solar radiation has to travel the farthest to get the D-Layer, absorption is usually fairly minimal.  
So far, during the middle of the day, we have moderate absorption, and good skip propagation.  
At sundown solar radiation no longer strikes our ionosphere from directly above, and ionization slows.  
This means there is less solar radiation to form free electrons.  
In fact, without this solar radiation, these free electrons tend to get attracted back to recombine with their host molecules.  
This is called "recombination".  
Recombination, when it starts to get dark, causes the free electron density to decrease, bringing the MUF down as well, which is why by total darkness, 10 meters (and soon thereafter 15 meters) are DX dead.  
The MUF falls below 28 MHz.  
The D-Layer is the first layer where ionization stops, since the sunlight no longer reaches near the surface of the earth, but is still illuminating (and ionizing) the ionosphere far above our heads.  
As the D-Layer goes into recombination, the free electron density decreases, and the absorption caused by those free electrons decreases.  
This is why signals appear stronger at night, because there is less absorption by the D-Layer during those hours.  
During twilight, aka the grey line: The D-Layer suddenly causes little absorption to signals passing through it, while the E and F layers are still being ionized by sunlight. This makes for about 45-60 minutes of interesting operating, especially for QRPers (low power operators). There is almost no signal attenuation, but the MUF is still very high, so long-distance skip is still possible. However, when the sun quits illuminating the E and F layers, the MUF can drop dramatically often with only a few minutes of warning. So when you establish a contact, get that QSL quickly.
Utilization: 
Time of day is the primary, but not the only consideration.  
Grey line propagation is generally north-south, but due to the inclination of the earth on its orbital plane it varies up to 23 degrees to either side of the north-south axis.  
Of course at the equinoxes (March 21 and September 21) the grey line runs exactly north-south.  
In mid summer and mid winter the gray line is tilted at 23 degrees.  
And so for you in the northern hemisphere your contacts in mid summer will be to the southwest, and in winter to the southeast.  
While not strictly a grey line phenomenom, from October through March, the north pole is in partial to total darkness, permitting over-the-pole, northern-hemisphere low- and high-frequency propagation between opposite sides of the earth.  
This is also true for the south pole and the southern hemisphere from March through October.  
Summertime propagation is totally different from the rest of the year, with HF openings and closings occurring much later in the day.  
The polar paths are primarily restricted to 40 through 15 meters in the summer, while transequatorial paths predominate on the low bands and on 10 meters.  
Generally, the low bands (1.8 through 10 MHz) exhibit best long-distance propagation from just before sunset, through darkness, to just after sunrise.  
The high bands (14 through 28 MHz) tend to open near sunrise, stay open throughout the day, and close after darkness.  
These openings and closings depend, of course, on solar activity, frequency and season.  
The ionosphere's behavior at sunrise and sunset is highly dependent on frequency.  
The 160-meter band is the most unreliable of all the bands on grey line.  
There may be no peak whatsoever at either sunset or sunrise.
160 meters: The 160-meter band has the shortest sunrise and sunset peaks of all the amateur bands.
80 meters: The 80-meter band exhibits a consistent pattern of signal enhancement beginning with first light, building to a maximum at official sunrise which may last from 10 to 20 minutes.
40/20 meters: The 40-meter band is the premier low-frequency band, with long-path openings to central Asia from October through March that are more reliable than 20 meters. Contrary to some published propagation material, 40-meter propagation does not peak to the west before sunrise but about 30 minutes after sunrise. In fact, propagation just before sunrise can be quite poor. Peak propagation spans about 30 minutes and drops off slowly for an hour or more.
10 meters: As pointed out in the technician license exam "from dawn to shortly after sunset during periods of high sunspot activity" is the best time for long-distance propagation via the F layer. However, in a solar minimum your best bet might be the grey line. In the eastern US this band will open to the southeast from just before to just after sunrise, depending on time of year and solar flux levels, and swing northward into Europe and Western Asia in another 15 to 20 minutes. From the eastern half of the US the best times to work central Asia on this band are usually within the first two hours following sunrise. In the spring and fall, there is often a long-path (southeast) opening to the Far East and the South China Sea region in the same time period.
In the late afternoon, the low bands begin to open in a direction across the approaching terminator (northeast in the northern hemisphere's winter) beginning with 40 meters as much as 2 hours before sunset. As sunset approaches, signals from the southeast become more and more audible. From just before sunset until total darkness, signals will peak along the terminator (southeast) on all bands from 160 through 20 meters. Long-path propagation to Southeast Asia is especially good on 20 and 40 meters during this period, and occasionally on 80 and even 160 meters.
Some of the challenges that you will encounter, especially on the low bands, include low activity (not everyone is as persistent as you), brief openings, atmospheric noise, E-region MUF, and absorption. In general, grey line contacts may vary from only a few minutes to 20 or 30 minutes maximum. Your window of opportunity will be brief, typically 45-60 minutes and can disappear very quickly. Upon contact get the QSL info before rag chewing.
A note for the vertically inclined:  Grey line propagation in the F layer will produce elliptically polarized signals thus affording a greater opportunity for those with vertical antennas.
Resources:
Real time graphics
and more graphics
provide real time graphic displays of the grey line projected on a globe.