Recent advances in computer technology combined with new theoretical methodology and algorithms have allowed for dramatic improvement in the computation of molecular properties. This has allowed computational chemistry to become a rapidly growing field of research, which plays a key role in many different areas of chemistry ranging from the interpretation of experiments, understanding of species that can be difficult or impossible to study experimentally (e.g. arsenic containing compounds and interstellar molecules), and chemical reactivity, to name just a few. Unfortunately, even with these advances, the extensive computational cost (i.e. computer time, memory, and disk space) of the sophisticated methods required to achieve a high level of accuracy effectively limits the size of molecules that can be studied to fewer than 10-15 atoms. Several approaches have been developed to help reduce the computational cost of expensive ab initio methods, and I will discuss several such methods including the correlation consistent Composite Approach (ccCA), hydrogen basis set truncation, and local correlation.