The last photos look like mulberry which is a tree, so not something you would want that near a building regardless of how you feel about mulberries. You can cut to flush with the ground and paint the cambinum (layer just under bark) with brush killer.

The first two photos look like privet, probably a golden type, either badly pruned or cultural problems (bad soil or not enough light for instance). In good circumstances, hard pruning privet can rejuvinate them, but they aren't a favorite shrub of mine, so I would remove them. They also look rather too close to the building.

foundation plantings are planted to hide the foundation .. NOT ON THE FOUNDATION... and that was prior owners first mistake ...

with good annual pruning ... some stuff can fit in that tiny bed ... but why privet??? ... that was their second mistake ...

bottom line ... they are badly planted.. the wrong plant.. overly mature ... and need to go ...

yes.. yo can make a 3 year renovation project of them .. might not be pretty during that time ... but lifes too short.. just get rid of them ...

the mulberry is a nightmare weed tree... i could send you a couple thousand seedlings if you want more.. get rid of it ...

increase the bed by 5 to 10 feet... and make a nice bed for some flowers ... if you want to work that hard ... and then leave 2 feet free and clear at the foundation ... taking into account the size of the plants you plant ...

ken

The top ones do look like a Privet of some description, Ligustrum. If you cut them down very low they will grow bushier from the bottom. But they'll never be particularly interesting.

Agree with floral; privet can be cut all the way to the ground and they will respond very quickly with new growth. However, they are a very boring, overused plant. Whoever planted them spent about three seconds thinking about it.

But, in some locations, that's all that is needed.

privet can be cut all the way to the ground and they will respond very quickly with new growth.

==>> but they will remain one foot from the brick ... and can easily make a 4 foot round ball every season ...

just to be the devils advocate.. they need to go ...

listen.. cut short ... watch for a year or two ... decide if you like the 2 or 3 shearings a year to maintain some small size ..

if you can live with it.. keep them ...if not.. sharpen your shovel ...

too many newbs.. think or want instant gratification in the garden ... most of us.. make a choice.. act.. and give the plant a year or two .. etc ... starting to repeat...

with knowledge.. now you can make a right decision for you .. let us know ... we bet on these things... lol ...

ken