Colorspace is three dimensional. In color management each color the human eye can see is mapped as an L*a*b coordinate. All the other color spaces fit inside of L*a*b. Some fit together better than others.

CYMK is the smallest gamut. The reddest red CYMK can print is 100% yelllow + 100% magneta which is not as intense a red as 255 in the red channel on a monitor. That is why when you print an sRGB file some colors, particularly saturated reds and purples, change.

sRGB was designed as a standard for color on a circa 1992 CRT monitor which displayed 256 colors. It is larger than CYMK, but a different 3D shape. Converting sRGB to CYMK is a bit like pounding a square peg into a triagular hole; the corners get bend or torn off. That's why the colors you see on the monitor don't match the print. You can't make a print match the sRGB monitor because sRGB gamut is bigger. But you can make the monitor gamut smaller to simulate what the print will look like. That's what the soft proofing mode in photoshop does.

Learning from the mistake of using sRGB as its default colorspace in an early version of Photoshop, Adobe created a new "working space" called AdobeRGB 1998. At the time there was no desktop device that could capture or display it all -- most monitors still can't -- but it was large enough to fit both sRGB and CYMK inside of it without any clipping of colors when converting from RGB to CYMK for printing. That is why it a better colorspace for camera capture if photos are eventually printed on paper with ink.

But since all but the most expensive computer monitors still only have a gamut roughly equal to sRGB or smaller an AbobeRGB file viewed in a non-color managed application like a web browser does not reproduce the colors of the original scene accurately. When a color managed application like Photoshop is used the monitor still can't physically display any the colors in the AdobeRGB file which exceed the montor's gamut, but the application will remap them to fit the monitor gamut in a way that is perceived to be "normal".

So if you shoot in Abobe RBG you are really only seeing slightly more than an sRGB version on your screen. And like sRGB what you see on the print will differ from what you see on the screen. But since CYMK fits almost entirely inside of the AdobeRGB colorspace there is minimal clipping of colors when they are printed.

The Cliffs Note's version of all of this is:

1) Shoot in AdobeRGB
2) Edit in AdobeRGB
3) Print from AbobeRGB whenever possible*
4) Convert files for web display and e-mail to sRGB

* Most 6-8 color inkjets are AdobeRGB compatible, but when printing commericially find out what color space the lab requires. If they support AdobeRGB files use it, otherwise they will be standarized on sRGB so Joe Megabyte's P&S files will print correctly.

The Purpose of Color Management

The goal of color management isn't to make a printer match a monitor, but rather allow a monitor to accurately simulate how the file will change when printed, and then control the process of change so grey tones remain neutral and the overall color balance is perceived to be the same even though the printing gamut is much smaller and limited.

The reason we do a printer profile from a file with known color values is to discover the limit of its gamut. It is what it is, and what it is differs from your RGB monitor phosphors / LCDs. CYM inks are not pure. If they were the K wouldn't be needed. 100% CYK = dirty brown, not black. C and M are not theoretically pure, they are cross contaminated. It's a problem which has vexed printers since the earliest days of color printing and why color management was developed.

If we use soft proofing and apply the printer profile to the screen image Photoshop will do its best to simulate how the file will look when printed: less saturated colors and less contrast than screen white/black. But even that simulation is limited because most monitors can't display some colors the printer can produce such as pure yellow pigment (which is difficult to mimic with green and red light).

The bigger the gamuts of the monitor printer, the less color will change from monitor to print. If we are editing on a cheap LCD with a gamut smaller than sRGB we might not be seeing all the color in a file in AdobeRGB. AbobeRGB is a working space that most CYMK gamuts will fit inside of. 6 and 8 color printers have bigger gamuts than a 4/C ink jet or SWOP CYMK (Standard Web Offset Printing) but all are still smaller than the outer limits of AbobeRGB.

If the color in our file is within AbobeRGB and the CYMK printing gamut it will not change when printed. But if a color is outside our monitor's gamut we will not be seeing it accurately and it will seem to change relative to the monitor appearance when actually doesn't. There are lots of yellows and greens in AbobeRGB and CcMmYKkk inkjet gamuts we will NEVER see accurately on a non-AbobeRGB monitor..

If a color is within the AbobeRGB gamut, but outside of the CcMmYKkk printing gamut it will change when printed to the closest color the CcMmYKkk can reproduce. But again it might also fall outside of the gamut our monitor can display; a double whammy reality of desktop color management with a cheap monitor.

The bottom line is, sadly, is that the printer gamut is what it is. And, it ain't gonna match our monitor unless the monitor displays the entire AdobeRGB gamut. If it doesn't the best we can do is soft proof as accurately as possible using a custom printer profile. Which takes us full circle to why you need the custom paper/ink profile; so Photoshop can show us, accurately how inaccurately our monitor displays how the file will actually print.

Using the OUT OF GAMUT (OOG) warning in Photoshop is like flying a plane in the clouds on instruments. The printer is the runway. When the printer profile is applied in soft proofing parts of the runway get hidden in fog. The fog is the parts of the screen image (limited by the monitor profile) which are grayed because they will not print accurately. The "runway" can be brought back into view by reducing the gamut of the file using selective color controls. For example if most saturated pure reds are showing an out of gamut on screen, reducing saturation in reds with Hue/Saturation will eliminate the warning. The red will look duller than it did previously, but it will print the same as it looks on screen (more or less).

Once all the OOG gamuts are eliminated the file displayed on the monitor should look like the print. If the gamut has been conformed to the printer gamut in soft proofing there's no need to convert it to the printers profile; everything already fits. Seeing the difference between the best the monitor can display and the best the printer can print is simply a matter of toggling the soft proofing on and off.

Perfect? No. Predictable? Yes.

It sounds awful, all those beautiful monitor colors not be visible on the print, but there's a silver lining; the human eye is easily fooled. Absent a side-by-side comparison with the monitor or a real fire truck a viewer will accept the red fire truck on the print as the reddest red on the planet.

Take a look at the color management section of one of my older tutorials. It explains the concept and historical chonology of color management and the differences between sRGB and Adobe. It also has some animated wireframe models of intersecting color gamuts which will help you visualize color space in 3D and how poorly sRGB and CYMK match.