It appears you have Foxtail Spear Grass if I am correct. The foxtail refers to the flowers, clumped together at the top. Search for "foxtail grass" or "foxtail spear grass" to confirm.
While the specific species varies, this can be bad if you have dogs, and for allergic people. The easiest thing to do is to remove them thoroughly by hand or using mowers and disposing of them with yard waste or in trash. It is not advisable to compost this.
You can use a herbicide after removing the grass, but herbicides themselves can be toxic. The best solution is to remove the grass entirely, and then mulch heavily. After the initial removal, it will be easier to identify and remove the new growths that sprout. Planting something else, like even putting down a lawn or growing other plants is also a good way of making sure that you achieve eventual control of this.
Note, that both you and your neighbor and anybody else close by, are best served by your mutual co-operation in timing and removing these things around the same time and laying constant watch. These things disperse their seeds through wind, through contact from your shoe soles, through animals, pretty much any way they can and thus you will need to stay on guard all the time.
Just as an example, I have removed these and other grasses from my landlord's yard, but because most of our neighbors don't care, we never have full control and every season, I have to run around and pluck these guys out throughout the growing seasons.
I forgot to add, when dry in large clumps, they run the risk of starting brush fires.
