The wikipedia Climate engineering page is informative.
The Carnegie Climate Governance Initiative (C2G) also has some informative info-graphics (one included below) and they don't appear to be secretly funded by gas companies (but it's so hard tell).
There's widespread hesitancy to look too seriously into these approaches because of fear that:
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They could serve as an excuse not to cut carbon emissions, or
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They could have unforeseen harmful effects.
The approaches largely divide into (1) reflecting incoming sunlight and (2) capturing carbon from the air.