At some point in the origin of life, life likely went through a stage where RNA acted as genome and catalyst-- the RNA world. Eventually, life evolved into the form we observe today, with DNA acting as genome and proteins acting as the main catalysts. Although there is no known direct evidence of RNA world organisms, we can gain understanding of life's early ancestors by creating catalytic RNAs in the lab that could have existed in an RNA world. This dissertation aims to develop and improve two of these catalytic RNAs (ribozymes). The first is a triphosphorylation ribozyme, a catalytic RNA that triphosphorylates the 5' hydroxyl groups of RNA using trimetaphosphate. In a RNA world, this activity could have been useful for chemically activating RNAs for ligation or polymerization. The second is a polymerase ribozyme, a catalytic RNA that catalyzes RNA polymerization. This activity could have been important for replication in a RNA world organism. In order to identify catalytic RNAs that can triphosphorylate their own 5' hydroxyl groups, an in vitro selection method was established. From a library of ~10¹⁴ random sequences, several active sequences were identified and one was analyzed in greater detail. This triphosphorylation ribozyme was modified to act in trans and had a reaction rate of 0.16 min⁻¹ under optimal conditions. Preliminary analysis of its secondary structure suggests that it forms a four helical junction motif. A catalytic RNA that catalyzes the polymerization of RNA was previously developed, but it is too inefficient to replicate itself. Its limitation is weak substrate binding. Here efforts were made to improve the polymerase ribozyme by reducing charge repulsion between the negatively charged ribozyme and its substrate using positively charged amino acids as cofactors. However, these cofactors did not improve ribozyme polymerization. An in vitro selection method that puts selection pressure on the ribozyme to bind its substrate in trans was developed to try to find improved polymerase ribozymes. Although no active ribozymes were found, several steps of a technically challenging in vitro selection method were established. In summary, this thesis presents work to develop two catalytic RNAs for a RNA world. An existing polymerase ribozyme was tested with amino acid cofactors and progress was made towards developing an in vitro selection that could be used to find novel polymerase ribozymes. Also, a novel catalytic RNA that can triphoshphorylate RNAs was created. This opens up new avenues that will deepen our understanding of the RNA world