\( sp^2 \) -related structures.

These are some important structures in which \( sp^2 \) bonding plays a significant role:

Also, here is a snippet from an intriguing site about bonding.  What we are doing is the "fairly high-powered stuff on the wave nature of electrons".
http://www.chemguide.co.uk/atoms/bonding/doublebonds.html#top

Be clear about what a pi bond is. It is a region of space in which you can find the two electrons which make up the bond. Those two electrons can live anywhere within that space. It would be quite misleading to think of one living in the top and the other in the bottom.
	Taking chemistry further:  This is a good example of the curious behaviour of electrons. How do the electrons get from one half of the pi bond to the other if they are never found in between? It's an unanswerable question if you think of electrons as particles. If you want to follow this up, you will have to read some fairly high-powered stuff on the wave nature of electrons.