Where is it a problem? And what are the problems?

Around here, clothes moths & meal moths are nearly the same size.

No problems as such at the moment except for the numbers. I'm just worried that they might pose some problem to my window plants in the future if they aren't going after my food or clothes!

Are they creating little cocoons that hang from the ceiling and walls that the catepillars then drag around with them? If so then I've had a similar problem but I can't help you with the identification. I can tell you how I got rid of them though. I found that the majority of the cats were living on the back porch in a metal cabinet that I keep gardening supplies in. To kill them I used a mix of dog shampoo and water in a spray bottle and then sprayed every moth that I found flying around inside the house and on the back porch. I picked the cats off the walls and ceilings by hand. I still have no idea what they were eating though since I never found them in my clothes or food. I don't have any plants in the house either due to my rather adventorous cats!

karalyn asked: "Are they creating little cocoons that hang from the ceiling and walls that the caterpillars then drag around with them?"

Those are case-making clothes moths.