The physical chemical principles underlying enzymatic thermostability are keys to understand the way evolution has shaped proteins to adapt to a broad range of temperatures. Understanding the molecular determinants at the basis of protein thermostability is also an important factor for engineering more thermo-resistant enzymes to be used in the industrial setting, such as, for instance, DNA ligases, which are important for DNA replication and repair and have been long used in molecular biology and biotechnology. In this talk, first the concepts of thermostability, factors modulating it, and thermostability engineering strategies will be introduced. Then, I will focus on a thermophilic DNA ligase from archaeon Thermococcus sp. 1519 and present my studies exploring the origin of its thermostability and thermo-sensitive regions using molecular modeling and simulations. In addition, I will talk about the protein engineering of this enzyme by predicting mutations that can enhance thermostability of the enzyme using bioinformatics analyses. Finally, some challenges in the field of thermostability engineering will be discussed.