These strategies deal with the root causes of climate change and involve reducing the amount of carbon dioxide already in the atmosphere (different from reducing the amount of carbon dioxide emitted). One method involves capturing carbon dioxide from ambient air, compressing it and storing it in geologic reservoirs (usually porous rock or depleted oil wells). However, at this point in time this strategy is considered too expensive to be cost effective (1).
Another strategy, known as Ocean Iron Fertilization, involves adding iron to the ocean in order to increase algal blooms. These blooms consume carbon dioxide as they grow, and when they die, they sink to the ocean floor, effectively sequestering the carbon. However, this method is highly controversial, because it is not known how long the carbon could actually be stored for, or the negative impacts it could have on the ocean ecosystem (2). An approach similar to this involves adding minerals like calcium or magnesium oxide to the ocean. These minerals react with acidic carbon dioxide, and increase the ocean's capacity to hold and store carbon. Another benefit to this method is that it also helps to reduce ocean acidification. However, as with all CDR strategies, there has been little research into long term effects (1).
CDR strategies are generally not the first ones considered by those who are interested in the use of geoengineering. These strategies are thought of as needing to occur on a very large scale over a long period of time in order to actually be effective. For this reason, they tend to be very expensive and not a viable option at this time.
Sources: (1) Caldeira, K. W., Keith, D. (2010). The Need for Climate Engineering Research. Issues In Science & Technology, 27(1), 57.