Peltiers are a tricky lot. They're kind of like water cooling was five or so years ago as far as being exotic and tricky.
Traditional cooling methods for electronics rely on the air surrounding the device for cooling. These methods are known as
passive cooling. This includes nothing (bare circuits), heatsinks, and water cooling.
A device with no specific heat removing device on it just relies on its packaging to dissipate enough heat. A heatsink helps this process by providing more surface area with its fins. The increased contact area with the surrounding air helps it to dissipate the heat of whatever it's attached to. This is the type most often used with processors, currently. Water cooling is just like a ginormous heatsink. The physical waterblock that makes contact with the hot device is smaller than high performance heatsinks and absorbs heat into the water instead of a metal fin structure. However, the heat in the water is transferred to a radiator (with a lot more contact area than a normal heatsink--thus its attractive cooling potential) where the heat is transferred to the surrounding air. Even though there is a pump, that isn't
active cooling. Water cooling is essentially just a big heatsink with the bulk of the dissipating material moved to a remote location.
None of those methods cools a device below the temperature of that air that surrounds the device (or radiator). In order of cooling potential, it's almost always (least to greatest): bare, heatsink, water cooling.
There are also two types of persistent active cooling common in computers. These types are phase change and thermoelectric. Phase change is just a fancy name for the system of cooling your air conditioner works. A refrigerant gas is inside a hermetic tubing system with an evaporator (the cold coil), a compressor (like a pump for water cooling systems, sort-of), and a condenser (the hot, dissipating coil). The thing about refrigerant gases is that when they expand, they absorb heat. They have the potential to go below room temperature by this process--which is both why it is appealing and also why it is dangerous. By continuing to drop a device below the temperature of the air which surrounds it, water can condense on that device's surface. It's important to insulate this type of cooling or strictly regulate it because of that danger. Insulating the device expands that temperature gradient enough to where water won't condense on the surface of the insulating material, inside the insulation itself (no moisture or outlet in closed cell foam [don't use an open cell foam]), or on the surface of the device (it's as cold as the insulation surrounding it). Insulation just plays a trick with the temperature difference to keep the dew point down at each level if enough insulation is used. The gas expands at a coil at the device, absorbing its heat and reducing the temperature at that point. The cold, expanded gas travels to the compressor where it is condensed in conjunction with the condenser coil back to a liquid. That warm liquid gas returns to the evaporator where the process starts over again. It's kinda funny--people thing the cold line goes into their house and the hot one comes out on their air conditioners. It's the other way around in reality, as odd as it seems without knowing why.
The other type of active cooling is called thermoelectric (aka peltier). In this method, two dissimilar metals form lots of small junctions. This is commonly sandwiched between two plates. When a DC electric current is applied, the heat from one side (one of the metal types) is transferred to the other (the other type of metal used). In theory, a TEC is capable of creating a 69 degree Celsius temperature difference between its two sides. Also, reversing the DC current (switch polarity) will cause the hot and cold sides to swap. A TEC is not a very efficient device when comapred to phase change. They output both the electrical energy applied to them as well as any heat moved. However, a TEC is a comparatively simple device that requires no gasses to operate, no noisy compressor, or sealed metal tubing. They do not leak, vibrate, or have the potential to poison their user like refrigerant based systems do. TECs must, however, be well cooled in order to work effectively, and they can easily burn out if inadequately cooled. For this reason, high performance cooling systems in computers using a TEC often cool the hot side of the junction with water cooling. As with phase change, proper insulation or regulation of the device is vital to safe functionality.
The appeal of low temperatures with computer components is that silicon based devices can operate at higher frequencies the lower their temperature. Temperature and clock speeds are not a magical reverse relationship. Making something twice as cold does not mean it will run twice as fast. The relationship is inverse logarithmic.
I can give more detailed information if you want it.