At a local level, they want at least police reform (including both greater accountability and transparency). Some want the police completely defunded, if not outright disbanded.
At the federal level, they want congress to take up meaningful legislative action and not just send a couple tweets and move on.
Ending qualified immunity would be a good start.
At the presidential level, they want acknowledgment that the problem exists and that he's making it a priority to address.
There has been some traction on the first - the second will be harder and takes longer - and the third has no chance with the current occupant.
I think the early protests were fueled by anger and frustration. Over the last week it has picked up so much steam that right now it is carrying on under its own inertia. And it's just a reality that the unemployment rate is 13.3% overall and 16.8% for black americans. That's a lot of people who currently have a lot of free time on their hands. Some basically view protesting as their new job - at least for now.
We're 5 months away from another extraordinarily divisive presidential election, at a time when the whole country is already a simmering pot of cabin fever. The Romans built the Colosseum so that the sport there would distract the people from revolting. Well there's no sports right now either. This thing isn't slowing down - it's ramping up.