NASA has put forward an interesting proposal to use a spacecraft with electric propulsion to redirect a small asteroid, or a large piece of a larger one, to high lunar orbit where astronauts could visit and examine it and bring back samples. By small, I mean something on the order of 500 tons. In comparison, the entire Apollo program brought back 382 kg or 842 lb of samples.
Here is an overview and fact sheet. Here are more details.
NASA has also proposed placing an outpost in Translunar Space, mostly based on existing hardware. Such an outpost would greatly increase the safety and efficiency of exploring such an asteroid.
It is probably the most interesting early manned mission we can do beyond Earth orbit. With an outpost, it compares favorably with the more difficult project of visiting a near Earth asteroid in its original orbit. Austere missions to the most favorable targets contemplate missions of six months or more for a five day visit to the asteroid.
It seems to me that if you are going to spend that much time soaking up radiation beyond the Van Allen belts, it's better to spend most of that time actually at the asteroid, and it's better to be seven days from earth in an emergency than 90.
One attractive consideration for this type of mission: more than half of the cost of bringing back the first asteroid is designing and building the spacecraft. Refueling it and replacing the capture mechanism to get another will cost much less.
Also, one of the benefits of the program is a considerable increase in the power and thrust capability of electric propulsion, which will be useful for many other potential missions.
We don't know nearly enough about the insides of asteroids. It appears that many are more like blobs of rubble than monolithic hunks of rock. It would be well to know them better before we are confronted with the need to divert one in a hurry.
If the first one brought back turns it to be mostly rubble, after everyone's appetite for rock and regolith samples is sated it might be very useful to run a series of controlled experiments to determine what kind of explosive and impactor force the remainder can take without breaking up into something more dangerous. For science!