Modern science has been grounded on reductionism at different levels from the very beginning. The reductionist approach still holds a significant influence on science, biology included, especially after the rise of molecular biology in the 1950s when biology went molecular, and life began to be interpreted as a molecular process regulated by genetic information. Reductionism resulted in becoming a very powerful analytical approach by which scientists were able to investigate many basic molecular and cellular processes. However as time passed, the limits of the reductionist project in biology have become increasingly evident. Under question was not the value of investigations at the molecular and genetic level, but rather the belief by which complex processes are reduced to certain molecules or genes and genome-phenotype relationships explained in terms of linear schemes. Life cannot be explained only on a molecular and genetic level. Biological systems should instead be understood as complex systems, which result from dynamic interactions of different components at different levels that operate as organized wholes. A different theoretical framework is required to study these systems that can lead towards a post-reductionist approach in science and biology. This paper discusses how the complexity theory can contribute to the development of this framework by providing a number of key notions, such as emergence, self-organization and complex causality.