Fig tree roots generally are very invasive, although much depends on the tree’s variety, its planting location, and the overall soil quality. Most fig trees, if they are planted in optimal conditions, spread their roots far and wide.

What varieties are less invasive when planted in the ground (keep their root systems more or less contained)?

Does the regular pruning help with this a little?

I see this as problem when planting a fig near a house or other structures. It also seems like impossible to get rid of them completely so I have to choose a variety wisely.

Have not heard of any problems with planting fig trees near a foundation or slab(maybe I missed the report or the post on such ??)...other trees, such as pine trees have been known to crack a concrete slab or foundation with their root systems if planted to close...on the other hand,my sister-in-law has had a fig tree planted right up against her garage wall(south facing)for nearly 25 years with no structural problems.

Not really invasive.
Invasive for me ,it means when you cut down and destroy plant,a thousand new plants come out from the underground root system,on a large area.
That never happen with ficus carica.
Something like ,Trumpet creeper,yes that is invasive,and will take years to  keep killing the new shoots,coming out of ground every year.

Different species of Ficus will be damaging though, I don't know the species but if you plant to plant anything other than common/symnra/san pedro figs, research to see.

I don't know anything about how invasive the roots are. But this video talks about it. He planted his fig trees right next to his house. Its the only video I've come across that talks about the roots spreading habits.

Wow, that's an eye opener.  I just posted a video of a huge fig tree growing out from under a crack of a house in Israel.  I really think this thing about figs needing to be close to houses or confined in some way is true.  You look at the places where figs come from and they're all very rocky.  I think fig trees need something to confine them for some reason and they'll grow better.  In the US we imagine the perfect growing conditions to be rich, dark soil and lots of room, but if you look at where figs come from the soil looks like desert conditions compared to what we have in most places of the US.  Tan soil and lots of rocky outcroppings is what they want I imagine.

Amazing video!
There are a lot of wild fig trees in California growing near mountains and in arroyos. They are all grow next to big trees or rocks, partially shaded. That is what they like.
That house in the video provides them a natural environment. I am not sure if the "leeching from the slab" elements make any difference though.
When I asked my question, I was mainly concerned about the house structure, dont want it to damaged. But now something interesting came out of this.

Many tropical ficus have very invasive roots. Ficus carica is not among the tropical ficuses.

Thanks, Jon.

I had another thought after the video (this is opposite to what I said above).
Maybe the cement/concrete in the slab IS leeching the elements that figs want? Would be interesting to run an experiment.
In the open, away from a house with slab, make a concrete columns and plant a fig near by. Will this make a difference?
In that video, the fig growing next to a pole was better than the figs in the grass but not as good a near the house.

Same way, you can add some small pieces of concrete to a container with a fig.

How does the concrete change the pH of the soil? Does it make more alkaline?  Yes, it seems so.

Looking closer at the soil we find that the soil is naturally very alkaline due to the presence of limestone or seashells. Sites that are near new concrete buildings or waste concrete may also be very alkaline. 

So, I guess, the success is in the soil's pH. The perfect pH for growing fig trees is a soil pH of 6.0 to 6.5.
Although figs can do well with many soils and tolerate acid or alkaline ph, figs seem to thrive in slightly alkaline soils.
The limestone (or concrete in our case)  supplies the mild alkalinity that the figs prefer.
Of course, the amount of the alkaline material you add to your soil depends on the original ph of your soil.