Abstract: Human activity, particularly the combustion of fossil fuels to provide energy, has led to a continued and well-measured increase in levels of atmospheric carbon dioxide over the last century, with increasing effects in recent decades. Many approaches have been proposed for reducing atmospheric carbon dioxide levels, including chemical direct air capture (DAC), ocean alkalinity enhancement (OAE), enhanced rock weathering (ERW), and biology-based approaches. Even with rapid emissions reductions, atmospheric carbon dioxide reduction (CDR) may be desirable to avoid excessive changes in Earth's surface temperature and climate. Fundamental physical constraints, however, indicate that such efforts will require extensive energy and/or material inputs. This colloquium addresses these considerations from a physical science perspective.