This review uses the giant muscle protein titin as an example to showcase the capability of molecular dynamics simulations. Titin is responsible for the passive elasticity in muscle and is a chain composed of immunoglobulin (Ig)-like and fibronectin III (FN-III)-like domains, as well as PEVK segments rich in proline (P), glutamate (E), valine (V), and lysine (K). The elasticity of titin is derived in stages of extension under increasing external force: Ig domain straightening occurs first (termed tertiary structure elasticity), followed by the extension of the disordered PEVK segments. At larger extension and force, Ig domains unfold one by one (termed secondary structure elasticity). With the availability of crystal structures of single and connected Ig domains, the tertiary and secondary structure elasticity of titin was investigated through molecular dynamics simulations, unveiling the molecular origin of titin's elasticity.