In this work, computational tools are used to investigate three issues in evolutionary biochemistry. After an introductory chapter, chapter 2 searches for short, ancient motives in contemporary proteins by focusing on the metal-binding character of aspartic acid; three such motives were found. The next issue is the structure of the genetic code. Refinements to the existing knowledge are contributed in chapter 3. The code belonging to the global optimum for error minimization in a widely-used code space (a long-standing question in the field) is determined by an exact method. Larger code spaces are formulated mathematically and investigated with an improved error function. This raises the debate over which code space should be used in this kind of studies. Most importantly, published possible scenarios concerning the evolution of the genetic code are shown to be all (including Crick’s Frozen Accident Theory) consistent with error-robust structure of the code. In chapter 4, the focus is on similar code triplets encoding the same amino acid. A hitherto unknown regularity in the standard genetic code is presented: No canonical amino acid is encoded by one single A-starting codon only, and this regularity, in combination with the wobble behavior of tRNAs with unmodified G-starting and C-starting codons, has implications for likely primordial tRNA sets. Chapter 5 introduces values to study the genetic code regularities with respect to molecular structure similarity of amino acids. In the final chapter, pan-editing in trypanosomes is investigated using computational tools.