Plants vary widely in their relative growth rate (RGR), be it dependent on environmental conditions or due to their genetic background. In a comparison of the RGR of grasses growing under different environmental conditions, variation in RGR tends to correlate with that in the leaf elongation rate (LER). When different species or genotypes thereof are compared under identical growing conditions, variation in LER may or may not correlate with that in RGR, depending on the comparison. However, since RGR is described by an exponential equation, whereas LER is mainly a linear process, we conclude that any correlation between RGR and LER must be fortuitous. That is. exponential growth must be due to increases with time in plant traits such as 1) leaf dry mass per unit leaf length invested per unit time, and/or 2) Sigma LER, i.e., the total LER of all the growing leaves at one point in time. The latter can be achieved as follows: 1) each subsequent leaf has a higher LER than the preceding one; 2) leaves appear at an increasing rate; 3) the duration of the process of leaf elongation increases for subsequent leaves. In this review, we only explore possible factors that account for changes in Sigma LER with time, in different genotypes and under different environmental conditions. Inherent variation in LER of individual leaves and variation due to environmental factors may reflect variation in the rate of cell division and/or in cell elongation.