What was done
In this review paper, the authors summarize the various plant rhizosphere responses to atmospheric CO2 enrichment that have been observed in several experiments.

What was learned
After compiling and analyzing recently published literature in this field, the authors were able to make several general observations about the impacts of elevated CO2 on plant rhizosphere components and processes.  Typically, atmospheric CO2 enrichment stimulates root growth, particularly that of fine roots.  Such increases in root production eventually lead to increased carbon inputs to soils, due to enhanced root turnover and exudation of organic materials, which can potentially lead to greater soil carbon sequestration.  In turn, increased carbon flow into soils tends to stimulate the growth and activities of soil microbial organisms that depend upon plant-derived carbon sources for their existence.  Finally, the enhanced activities of fungal and bacterial plant symbionts often lead to increased nutrient acquisition for plants.

What it means
As the atmospheric CO2 concentration increases, nearly all of earth's plant life will respond by exhibiting increased rates of photosynthesis.  The additional carbon thereby removed from the air is often used preferentially by plants to increase their belowground biomass, especially that of fine roots.  Because fine roots are involved in the exudation of organic compounds and have a relatively short life span, large amounts of carbon are input into soils where it can potentially be sequestered away from the atmosphere.  In addition, increased soil carbon contents often stimulate microbial growth and activities, which can increase soil nutrient availability, ultimately enhancing the growth of plants.  In summary, increases in the air's CO2 content stimulate plant photosynthesis and growth, which positively affects rhizosphere components and processes, which in turn feedback to positively impact plant growth yet again.