In the last 25 years, computational chemistry has become a fundamental research methodology in all areas of nanoscience. Computer simulations are powerful nano-scopes that can reveal details of molecular processes on lengths of space and time inaccessible to experimental observations. Along with clarifying the physicochemical properties of single molecules or systems, they provide insights for helping the design and manufacturing of new nanomaterials and nanodevices. Among the various computational methods, molecular dynamics (MD) simulation is a powerful approach to analyzing structural and dynamic properties of nanomaterials at different time and space scales. This chapter aims to provide a general and concise introduction to the MD simulations of molecular systems by showing some examples of applications for studying biological macromolecules and nanomaterials.