From near the very beginnings of Evolutionary theory, scientists have assumed that life arose in something called "prebiotic soup" -- a watery mixture of chemicals that (somehow) brought rise to life. Many people have pointed out that there are a large number of steps that seem very improbable for the creation of life, and only a the first stages (e.g. creation of amino acids from basic components) have been demonstrated in the lab.

But scientists are slowly getting a grip on the next stage as well -- linking (or polymerizing) the amino acids together to form peptides, polypeptides, and eventually proteins. A useful hundred-amino acid protein might seem impossible to form by chance, but scientists now realize that instead of random trial-and-error, auto-catalytic sets of proteins and enzymes could emerge that would catalyze their own production, and natural selection could start working! Once this happens other steps still need to be worked out (i.e. what came before an RNA-world), but there's still a missing step in the middle: how did polypeptides get long enough to act as enzymes that could catalyze their own production?

One reason this is a hard problem (apart from the right- and left- handed stereoisomers of each amino acid) is that there is an opposite process to polymerization: hydrolysis. This is the breaking apart of amino acid chains by water, and it is how we are able to digest food. This process competes with polymerization, and does not allow long polypeptides to form... unless a mineral template is used, such as clay.

A good link with more details.