What are the commercial laws for things like vintage ads, posters, and art?

For example, could someone make a piece of art using a part or the whole of a vintage ad, and then sell that art, or does someone most likely own the rights to old graphic advertisements?
What about reproductions or replicas? Is it illegal to sell prints of famous pieces of art? Could someone take something like this and slap it on a t-shirt and sell those?

I know that I often see posters, prints, calendars, items with famous art pieces mass produced and sold – how does that work, legally?