Many people have thought of biofuel as the ideal way to replace petroleum fuels. Biofuels can be liquids, and in fact, "liquid fuel made from biomass" is the most common meaning of the term. Because the focus here is on liquid carbon, liquid forms are the biofuels of interest. Examples include ethanol and biodiesel.
Basic chemistry tells us that the amount of CO2 released when burning liquid fuels is essentially the same for a given amount of energy provided. However, the common view is that biofuels are inherently carbon neutral. That's because the CO2 released when the biofuel is burned is offset by the CO2 that was taken up from the atmosphere when the fuel's biomass feedstock was grown. Combine this fact with the fact that biofuels can be produced from home-grown biomass, and it's easy to see why biofuels have such enormous appeal as replacements for oil.
From a climate perspective, it's this recycling of CO2 that makes biofuels of such special interest. Recognizing the inefficiencies and other adverse side effects of synthesizing biofuels from crops used for food and feed such as corn and soybeans, there has been a broadly supported effort to turn non-food biomass into convenient liquid fuels. Cellulosic ethanol, for example, has been for many years a holy grail of biofuels research. The end product is still ethanol, chemically identical to ethanol now made from corn or other starch-bearing plants; it's known as cellulosic ethanol because it is made from various forms of cellulose that make up the bulk of plant matter. Much more of a biomass feedstock -- not just the plant's naturally produced sugars, starches or oils -- can then be turned into fuel, as can organic wastes including harvest residues, forest trimmings and much of what is in garbage.
But are biofuels the only way to accomplish recycling of CO2? And more generally, whether or not CO2 is literally recycled through a product and its associated production process, are there ways to take CO2 out of the air in order to counterbalance the CO2 emitted when a fuel is burned? The answer is yes.
Posing the question this way, i.e., inquiring about the options for more generally counterbalancing the liquid carbon that is inevitably released when a carbon-based fuel is burned, opens up a wider range of possibilities.
One is to simply regrow forests or otherwise restore and replenish the carbon stocks that build up on land through natural plant growth. There's quite a literature on this topic and a lot of effort goes into ensuring that such carbon sequestration in the biosphere is done properly, to be sure that any claimed CO2 uptake is real. The topic is that of forest carbon offsets, which can take various forms and more broadly fall under what is known as terrestrial carbon management.
Another is carbon capture and storage (CCS), commonly referring to mechanisms for adsorbing CO2 from smokestacks or other concentrated sources and then storing it underground in geologic formations. No practical means exists for capturing CO2 from vehicle tailpipes, so electric power plants and other industrial sources are the main targets of CCS efforts. As it turns out, because fermentation releases CO2 (think of beer bubbles) and does so without contamination by pollutants from combustion, ethanol plants are an excellent source of CO2 for CCS. Demonstrations of this concept are underway, e.g., in a CO2 capture project at an ADM ethanol facility in Illinois.
One of the places to store CO2 underground is in an oil field. In fact, pumping CO2 into an oil field in order to squeeze out more oil is an established technique for enhanced oil recovery (EOR). If the process is designed and managed so as to keep nearly all the CO2 used for EOR underground, then it counterbalances at least some of the CO2 released when burning motor fuels produced from the oil extracted by means of CO2 EOR. CO2 EOR has actually been used for many years to boost oil production. Historically, however, it used CO2 that was itself extracted from the earth and the process was not necessarily managed to keep the injected CO2 underground, and so it didn't counterbalance the CO2 from combustion of petroleum products.
In any case, the point here is that the use of biofuels is one instance of a more general category of approaches for counterbalancing the CO2 released when carbon-based liquid fuels are burned. In addition to forest regrowth and CO2 EOR, other options exist as well.
Some might dismiss approaches based on some form of sequestration (either terrestrial or geologic) as not relevant because they either don't produce a fuel or don't replace petroleum. The desire to replace petroleum is indeed a consideration, and a politically resonant goal for many years. However, it's not the same as the carbon concern, and taking a strict look at the core problem of carbon imbalance means that all options for counterbalancing CO2 emissions need to be on the table.