Chemical reactions occur when the outer electrons of an atom interact with the outer electrons of another atom. Atoms also want to achieve an electronic configuration which results in their oute shell of electrons being completely full. (Which for almost all atoms equals an outer shell comprised of 8 electrons. Hydrogen, Helium, Lithium, Beryllium, and somtimes Boron and rarely Carbon are the exceptions to that rule and are happy with just two outer electrons). So the atoms will react in order to acheive the electronic configuration of their nearest noble gas. This is why the halogens and the alkali/alkaline earth metals are so reactive. The halogens just need one more electron to obtain the electronic configuration of their nearest noble gas, and the alkali metals really want to give up their lone extra electron in order to also get a noble gas configuration.
You also need to remember that the nucleus of an atom has a positive charge, and the electrons have a negative charge. So the electrons will be attracted to a higher positive charge. The halogens, especially fluorine, have a very strong effective nuclear charge. That means that their nucleus is very readily felt by their electrons, and the electrons of other atoms. As a result they generally tend to form ions with a -1 charge as they get the electronic configuration of their nearest noble gas. Alkali metals are the opposite. They have a relatively weak effective nuclear charge so their lone outer electron tends to feel the presence of other atoms' nuclei as opposed to their own. Now what the heck does this have to do with the noble gases?
The noble gases show a pretty strong effective nuclear charge, but it is perfectly counter-balanced by the full outer shell of electrons they have. As a result, the electrons from other atoms can't really be 'pulled' by the noble gas' nucleus, and the nucleus of other atoms generally don't have enough of a pull to grab an electron from a noble gas atom. However, this isn't the case for the heavier noble gases. As you may recall from general chemistry classes, the reactivity of the alkali metals increases as you move down the group, and the opposite is true of the halogens. The alkali metals increase in reactivity because they want to give up an electron, while that of the halogens decreases because they want to take an electron. The one common trait you can pull from this has to be a weakened effective nuclear charge. The reason why the force felt by the outer electrons from that atom's nucleus is weaker is because the further down a group you go, the more electrons there are around the nucleus. Like repells like, so the electrons kind of buffer each other. As a result, on atoms like cesium that lone outer electrons feels almost no pull from the nucleus and will easily jump ship and cause a 'reaction'. With iodine, its nucleus generally doesn't exert much of a pull on other atoms' electrons, so it has a harder time in terms of reacting with other elements. This is all caused by the shielding effect that those electrons have on each other.
With the noble gases like radon, xenon, and krypton, they have a good number of electrons surrounding their nucleus. As a result, those outer electrons don't feel as strong a tug from their own nucleus as the outer electrons of atoms like Helium, Neon, and Argon do. Therefore, if you take an element that exerts a very strong pull from its nucleus (like fluorine does), you can get that other element to pull an electron off of those noble gases and make them react. Highly reactive compounds containing fluorine atoms, as well as elemental fluorine, are mixed with the noble gases and allowed to react. The fluorine atoms pull an electron off of the noble gas giving it a positive charge and the fluorine atom a negative charge. Charges are balanced and everybody is happy. However, these noble gas compounds are not all that stable and will readily decompose back into the noble gas and fluorine.
So in a sense, it's the size of the noble gas atom that determines the ease of its reactivity. Xenon, Radon, and Krypton are fairly big atoms so their outer electrons are more apt to be pulled off by a strong electron grabbing substance.