A followup question might be: how much does neoliberalism allow capitalism to abandon states, that is, nation states? — Jamal
I think the state remains as important as ever. What does happen though, is that the state fundamentally changes in its function and orientation. Where once it functioned - at least in the West - as a social bulwark to market generalization (via social security, investment in infrastructure, efforts at redistribution, etc), it now functions more and more as a simple police apparatus. That is, instead of taking care of your population, it's much simpler to punish and incarcerate them. As it so happens, the latter affords more opportunities to profit, even though it may, in the long run, be more expensive for all involved. Related to this, the rights of property above all else are the focus of state action: the state exists to protect - and expand - property rights. All other rights - like say, rights to be in control of one's own womb - are negotiable. Workers rights above all, are subject to destruction by states, instead of protecting them. It is a concerted and sustained political effort.
On the foreign policy front, the is state still vitally important to maintain overseas markets, along with expanding the reach of 'open markets'. This usually means negotiating so that companies have access to production in poorer - although somewhat stable - countries like China, Indonesia, or Vietnam. It takes enormous state organization to ensure that all this happens smoothly so products can be manufactured there and then shipped in to the core nations. And then of course these war to subdue threats to market generalization - which is a partial explanation of what is happening in Ukraine right now.
And the other thing states do, more and more - I think maybe among the most consequential and least talked about - is to take on private risk. That is, private business risk is 'offshored' to state, who bear the burden when capitalist markets fuck up. The political economist Daniela Gabor has a really, really
excellent and easy to read paper [PDF] on this topic. From the abstract: "The state risk-proofs development assets for institutional investors by taking on its balance sheet: (i) demand risks attached to commodified (social) infrastructure assets, (ii) political risk attached to policies that would threaten profits, such as nationalization, higher minimum wages and climate regulation, (iii) climate risks that may become part of regulatory frameworks; (iv) bond and currency markets risks that complicate investors’ exit". This 'taking on investment risk' tracks with the increase of financialization: states can function as lenders of last resort and prop up 'too-big-to-fail' institutions without which everything goes tits-up.
One thing to note is that while states are important, this has very little to do with state
sovereignty. States do all this, but not because they are sovereign, but because they are largely held hostage by market forces: states are largely the bureaucratic systems of market actors in all of this. This is most clear in places like the EU, where states more or less simply do not have control of their own fiscal or monetary policies. Which again means, in lieu of actual governance, they are reduced to a simple security apparatus. International "trade agreements" like GATT and NAFTA do the same on a global scale. So there's a kind of separation of 'the nation' from 'the nation-state'. Insofar as nations have anything to do with it, it's as a scape-goat: nationalism blossoms to compensate for the abandonment of the state for the people. Instead of blaming capitalism, migrants, minorities, sexual deviants, and colored people are blamed for decaying societies. The separation of nation and state makes the nation something deadly.
Also I haven't said anything about currency but oh boy states and currency and the necessity of states to try and keep currency under control for the sake of markets has basically driven the last 80 years of global history.