I can't tell if those leaves are tiny but if they are, it might be wire vine (some people call it angel vine), sold as a houseplant in decorative little pots in nurseries. I saw it some years ago in San Francisco when I was getting near Baker Beach and it covered a whole hillside in late summer. Min

Yes, it is Wire Plant, Muehlenbeckia axillaris. I grow it in pots and barrels, but it escapes occasionally and I have to dig it out. As far as removal- it depends upon where it originates- if it is coming from a neighbor's property, you will have to monitor the property line. If it originates on your property, you can just dig it out. I imagine it also dies if you spray it with Round-up, but you would have to be persistent, because the dead-looking stuff underneath will sprout fresh green leaves after the top is killed. This stuff is used on freeway banks to cover them- so you can imagine how big a plant gets.
Renee

Used as a drought-tolerant groundcover.

To you it is a pest while to me it is my lovely ground cover.

I like the looks of this. I have been using Bacopa for a ground cover but I don't like the smell at all. Does this wire plant have a scent ?

No scent so far but it would have to be in a large area. This is not something you mix in a flower bed.

just because a plant is vigorous doesn't mean it's invasive. This plant isn't listed as invasive in Cal-IPC.

wire vine had it on a fence in my backyard, it grew up the redwood tree , mounded on the fence , my children could jump on it like a mattress when it was mounded up. it was terrible. i had to use an herbicide to get rid of it.this was before the invention of roundup which i don't routinely use. we cut as much as we could and sprayed it with brush kill which kills poison oak, it keep coming back so you have to keep on top of it for a couple of years. after about 2 years we got rid of it.

Perhaps invasive isn't the right word, if that has a specific meaning. I would call it a garden thug, at least in my conditions. I like it enough to keep it, though.

I don't deny that it is a spreader. I routinely trim the edge. Same as one would do with Bermuda grass. I control it's growth by not watering it. It can get much taller but I mow or shear it when required. Someone mistook it for dichondra and I was delighted.