The micropillar compression test is a novel experiment to study the mechanical properties of materials at small length scales of micro and nano. The results of the micropillar compression experiments show that the strength of the material depends on the pillar diameter, which is commonly termed as size effects. In the current work, first, the experimental observations and theoretical models of size effects during micropillar compression tests are reviewed in the case of crystalline metals. In the next step, the recent computer simulations using molecular dynamics are reviewed as a powerful tool to investigate the micropillar compression experiment and its governing mechanisms of size effects.