Spray with neem oil. Mix as directed and make sure it comes from the seeds of the neem tree and not the leaves or bark.You should be able to find it at any big box store in the insecticide section.

what the heck are those things? some kind of mite? What kind of plant are they on and in what conditions? and how long did it take to get like this?

Ditto jcrowder!

Wowsers. I've never seen so many aphids in one place. Lots and lots and lots of cabbage aphids.

Why spray when you can use a directed water spray to remove them. Or, if you feel particularly nasty, you could squash the living daylights out of them.

That said, it looks like the plant might be completely engulfed in aphids. If so, remove plant, toss in trash.

I think it's history. And this is SO annoying because it was purple broccoli with 270 days to maturity. it is just starting to put out "buds". But having looked at these photos-I could never eat them anyway.
I had not been able to really look at the plant for 2 weeks, what with all the rain and working late. But I probably wouldn't have noticed them at the start anyway. I thought it was mold from all the rain, and assumed it would go away when the weather dried up.

Yes they are aphids.

Why spray when you can use a directed water spray to remove them

Because spraying with water can drown the plant, won't get them all and doesn't break the life cycle.

Tossing the plant is extreme but if you can't get past the aphids then toss it.
I pick veggies and eat them while in the garden. A little protein never hurt anyone. lol!

A little? I will be happy to share my extra protein with anyone who wants it! LOL

honestly, I'd use my fingers to smush them and wipe them off. Gross, but effective. If you're more squeamish, coat the plant with insecticidal soap. Or you could give up, I guess, if you are grossed out by eating it now. I bet they'd be just fine with a few thorough coatings of soap and water spray, though. You've already invested so much time in them.

You could always serve it to unsuspecting dinner guests. LOL. Kidding. Sort of.

Ok, I ripped out the plants that were too far gone. I still have a few that are kinda bad, but worth trying to salvage. Can I use a dish soap:water mix? If so ,what is the ratio?

The general recommendation is 1 tsp of soap (castille or fels naptha, for example) per 1 quart of water. Some people use up to 1 Tbsp per quart, and some use dishwashing detergent, and others buy insecticidal soap at the store (the bottle I bought a few years ago was Safer brand, and I think it included a pesticide in addition to just soap). Using a homemade solution that's too strong can burn the leaves, so be careful.

I hope they pull through. I have a soft spot for purple vegetables. :)

Use Dawn or Joy dish washing liquid. Not the antibacterial stuff.
I use 1 tsp per 24 oz spray bottle.

I will go and buy one of those brands. Is one better than the other?

Not sure but I use lemon scented Joy. Works well on spidermites too. If it's not working to your satisfaction try rotating soap one week and neem the next etc. etc.