Name that car part

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What are these little blue and grey caps called? What do they do? Are they part of the cooling system? What happens if they are not there?
Ellen's 2001 Eclipse is overheating now and then. Her coolant reservoir is empty, we filled it. The radiator seemed to still be full of coolant. Near the coolant reservoir there is a metal pipe/line that looks like it has one of these little caps missing. There is also a short hose coming out of the reservoir that is not attached to anything but we assume this is an overflow hose, are we right?
The picture above is not Ellen's car, it is a later model Eclipse.
UPDATE: It may have just been a radiator hose that was loose. Which makes me happy because that's about 1000% less expensive than if the coolant was mixing in with the engine oil (which would point to a blown head gasket). Thanks for everyone's responses and descriptions of cooling system pitfalls. As for the little blue and/or grey caps, they're probably just covers that keep dirt out of fittings and aren't much to worry about.
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