Mr Donald Rumsfeld, the American Defence Secretary, has announced that the "skies are now free for US planes".
In the next phase allied aircraft can move, reconnoitre, photograph and attack almost without inhibition if not completely without risk.
The survival of a missile system is always possible, but vigilant fighters will fly escorts. Snatch landings of Special Operations troops may now be tried.
So, what next? History warns against ground operations in Afghanistan, although the coalition aims are not those of Britain and Russia in the past.
Occupation is not intended. Even limited areas such as airfields would be reluctantly taken over. Guarding them would take infantry. Losses by sniping would be morale-damaging over a period.
There are signs of doubts about killing or capturing Osama bin Laden. If he survived a protracted hunt his myth in the Arab world would grow. Mr Bush's unprecedented popularity might fall, like his father's. Bin Laden's death at Afghan hands would be preferable.
Destroying the Taliban government, exiguous though it is, remains a war aim. Afghanistan's economy, roads and telecommunications, can be dominated electronically and from the air. The Taliban organisation can be hassled from pillar to post. Leaders can be bought - this may require agents on the ground.
It won't be easy.
The Northern Alliance can be got to Kabul. It can be given military support and prodded towards elections and democracy, while US aircraft sweep over the mountains to strike any Taliban gatherings. The coalition will probably accept any stable regime so long as troops don't get bogged down and attention can be focused elsewhere.
The Jerusalem Post says Israel is supplying America with "an extraordinary amount" of intelligence, especially about countries such as Uzbekistan and Kazakhstan.
Israel has immigrants from there, plus human and electronic resources devoted to Iran.
What about the "wider web of terror"?
There are scores to settle in Iraq and Iran. The weapons and troops are in the area. It must be tempting to push the opportunity to see all opponents broken together.
What of the Taliban foot soldiers? They carry the ubiquitous Russian Avtomat Kalashnikova - the Kalasknikov assault rifle, or AK47.
This has been the most successful weapon of its type and is the most widespread in the world.
After the war, the Soviet army considered accuracy at 300 to 400 metres was enough. High volume of fire, simplicity in training and reliability were essential.
Ability to fire on the run over the last (and often fatal) 300 to 400 metres of an infantry assault was also needed.
Mikhail Kalashnikov designed the AK47 accordingly. Its bayonet doubled as a saw and a wire-cutter.
A variant with a folding butt became popular with guerrillas because it could be concealed.
The traditional gunsmiths of Afghanistan can make many of the spare parts.
At the other end of the scale there is the "Stealth" aircraft. The "flying wing" B2-A and the F-117A aircraft are examples.
In simple language Stealth aircraft are difficult to pick up by radar or infrared detectors or to hear and see.
The peculiar appearance of the B-2A bomber is mainly intended to reduce "radar signatures". When a radar pulse strikes a plane some of its energy is absorbed, some scattered and some reflected back to the radar antenna.
Coating an aircraft with radar-absorbing materials reduces the energy for reflection back.
Sloping and curving outer surfaces so that energy is scattered also helps.
The B2-A can fly almost 3,000 miles on one fuelling. It can hit any target in the world (except, perhaps, parts of China) and return to base in the US.