Usually in cycloadditions, we find that there are two components involved: they are known as the diene and the dieneophile.  In a similar fashion to electrocyclic reactions, we can tell if a cycloaddition is feasible by inspecting the HOMO and LUMO.  Here is a very simple case:

HOMO (Ψ2)			LUMO (Ψ3)
LUMO (Π*)			HOMO (Π)

The lobes that are about to interact with each other in this example, as you can see, are of the same phase.  Both examples are of the same species in this example.  The two cases merely illustrate that it is irrelevant which species is said to be using its HOMO, and which is said to be using its LUMO.  This type of situation, where the phases are the same, and form bonding interactions, is called symmetry allowed.  If however, we chose a situation where the phases of the lobes were not correct, it would be a case of a symmetry forbidden reaction:

	LUMO (Ψ3)
	HOMO (Ψ2)

The case above of the HOMO and LUMO of two dienes is an example of a symmetry forbidden reaction.

In general, we find that reactions involving 4π + 2π electron systems are thermally symmetry allowed, whereas those involving two 2π systems are thermally symmetry forbidden.

As we have already seen however, the photochemical cycloaddition below does work, though the thermal equivalent is symmetry forbidden:

 A classic example of the 4π + 2π cycloaddition is the Diels Alder.  This reaction proceeds exclusively with syn addition:

As we can see from the diagram, syn addition must occur to line up the orbitals correctly.  This is also due to the fact that this reaction is concerted (i.e. all steps occur at the same time).

Another important point is the stereochemical selection of the endo product over the exo, despite the fact that the exo is thermodynamically more stable:

The endo product is normally (although not always) the major product, despite the lower energy of the exo.  The reason for his is that the endo product proceeds via a lower energy transition state, even though the final product is of higher energy. Explanations as to why the endo transition state is lower in energy vary, but it is likely that there is some form of secondary interaction between the lobes of the HOMO and the LUMO, but which do not result in bond formation.  These interactions do not occur in the exo transition state, because no overlap between the orbitals concerned is possible.