Self-organization in biological nervous systems during the lifetime is known to largely occur through a process of plasticity that is dependent upon the spike-timing activity in connected neurons. In the field of computational neuroscience, much effort has been dedicated to building up computational models of neural plasticity to replicate experimental data. Most recently, increasing attention has been paid to understanding the role of neural plasticity in functional and structural neural self-organization, as well as its influence on the learning performance of neural networks for accomplishing machine learning tasks such as classification and regression. Although many ideas and hypothesis have been suggested, the relationship between the structure, dynamics and learning performance of neural networks remains elusive. The purpose of this article is to review the most important computational models for neural plasticity and discuss various ideas about neural plasticity's role. Finally, we suggest a few promising research directions, in particular those along the line that combines findings in computational neuroscience and systems biology, and their synergetic roles in understanding learning, memory and cognition, thereby bridging the gap between computational neuroscience, systems biology and computational intelligence.