Early methods of replication probably would not have allowed the dilution of enzymes after every "generation" so early life could build on the past.

Name to remember:  Cech and Altman
Period to remember:  1980s
Feat to remember:  discovered ribozymes, ribozomes with enzymatic capabilities.  this leads scientists to believe RNA (which can theoretically replicate itself) is the simplest and thus the most plausible first replicating genetic material.  

This is supported by RNA abiotic synthesis in which sequences are 5-10 nucleotides long with only RNA monomers present and up to 40 nucleotides long with less than 1% error with zinc present to act as a catalyst.  In the application of natural selection to molecular genetics, some RNA are more stable in a environment and thus replicate more than the other RNA units and the descendents will be similar strands evolving with the copying errors that pop up.

Panspermia:  Life from Space.

Supporting this, organic compounds such as amino acids have been found in modern metorites.  Extraterrestrial organic compounds are known to form small vesicles when mixed with water.

Challenging the RNA theory is the fact that even under optimal in vitro (artificial, e.g. test tube) conditions it is difficult for make RNA without enzymes.

Name to remember:  Julius Rebek, Jr.
Location and Date to remember:  Massachusetts Institute of Technology, 1991
Feat to remember:  a simple self-replicating molecule was designed (see figure below).

Next:  "Archae and Eubacteria."