Many plants have the ability to readily produce clones. A piece of stem, root, or leaf will result in a new plant. When a leaf cutting is collected the new plant is composed of adventitious growth. The leaf develops a meristem and produces dedifferentiated parenchyma cells. With time those parenchyma cells differentiate, becoming adventitious shoots and adventitious roots. A new plant is formed.
Many succulent plants grow well from leaf cuttings. Some examples are Hylotelephium spectabile (showy stonecrop)  and Sedum rubrotinctum (jelly bean plant). Here are some pictures of these plants at Cal Poly. The stonecrop is in a garden in the learning Pine Arboretum, the jelly bean plant is in flats in the production area.
Leaves may be collected and stuck in a propagation medium. In these photos you’re seeing a 9:1 mix of perlite and sphagnum peat moss. The basal part of the leaf is stuck in the medium.
Formation of adventitious roots should occur quickly, followed by the emergence of adventitious shoots.
Leaf cuttings are slower than stem cuttings with these two plants. Stem cuttings do not require adventitious shoot growth. It’s pretty cool to grow an entire plant from a leaf.
 Thanks to crosses between Hylotelephium spectabile and H. telephium it is very difficult to identify stonecrop specimens in a landscape. The plant that I am showing may very well be a hybrid. The name of the most popular hybrid, H. × ‘Herbstfreude’ (‘Autumn Joy’ in translation), is often attributed to plants that are mere posers.