There are many forms of sugar art.  Some of the most popular are Color Flow, Gumpaste, Royal Icing, Fondant, Buttercream transfer, Chocolate Transfer, Edible Image
SUGAR ART
GUMPASTE is a different form of Sugar Art and can be very labor intensive.  Flowers are made by rolling out "sugar dough" and using cutters to create the petals.  They look very realistic!  It is not advisable to eat this type of sugar art as it dries very hard like cement and is tasteless.   Here are some samples of flowers in gumpaste.
COLOR FLOW  is a technique where you create a picture in a "liqud sugar" type form.  The picture is made by flooding a picture with colored liquid icing, which will dry to a hard finish.  The piece can be put on top of a cake, and then eaten like candy.  Here are a few examples that I have done
ROYAL ICING is very similar to the color flow but you can do more 3-dimensional things like flowers.  It dries hard but you can actually eat the flowers, plaques or shapes as it is a pure sugar based type of candy.   Here are some samples of flowers in royal.
You can also create 3-D molded figures.  Here is a sample of teddy bears
BUTTERCREAM TRANSFER is very similar to the color flow but you are making the picture from buttercream icing.  It is one of the easier, basic techniques to having an edible picture drawn onto your cake.  Here are some samples
CHOCOLATE TRANSFER is very similar to the other transfer techniques except you are making the picture out of chocolate  It is totally edible and delicious!  Again, it is one of the easier, basic techniques to having an edible picture drawn onto your cake but a litte more expensive than buttercream transfer.  Here are some samples
EDIBLE IMAGE  is done by using a special printer with food grade ink.  Any picture can be copied onto the icing sheet and applied to your cake just like a sticker!  They are completely edible.  Here are some samples
GALLERY OF OTHER CUSTOM MADE PIECES
PARTY ANIMALS !
(Commissioned piece by Teresa M.
Minecraft Cake featuring edible images of Creeper, Endermen, Steve, Pig and TnT blocks.  Figures commissioned by Teresa M