Abstract: The elastica model of slender rods exists widely in nature and engineering applications, such as submarine cables, high voltage transmission lines, compliant ropes, springs, drilling rods and oil suction rods in petroleum engineering, nano-fibers and nano-tubes, DNA and high polymers, stems in climbing plants. It is more challenging to analyze the deformation of the elastica of slender rods, which are normally accompanied by strong geometry nonlinearity. The history of elastica proves really dramatic. It has lasted almost 8 centuries up to date, and there were a lot of distinguished scientists involving in this problem, from the viewpoints of mathematics, mechanics and experiments, etc. In this paper, the history of elastica is introduced spanning from planar elastica, spatial elastica to the analogies between elastica and some other physical phenomena. The history of elastica can help us understand how mathematics and mechanics are closely combined with engineering technologies in face of engineering applications.