For the past 50+ years, frames have been integrated with bodies on all cars and some trucks (unibody). The exterior shell of car bodies is a mix of materials, including plastic. The interior shell of body interiors contain very little that's recyclable without an ambitious amount of disassembly that would be very costly. I don't see car recycling happening until something like another world war makes it worth the effort.
The shells are crushed and shredded after economically separable discrete parts have been removed. Magnetic and eddy current separation is used to break out ferrous and non-ferrous metals from the shredded pieces. The plastic bits are as hard to recycle as any plastic, but most of the metal can be effectively recycled.
In the United States, more than 95% of the 10-15 million scrapped vehicles annually enter a comprehensive recycling infrastructure that includes auto parts recyclers/dismantlers, remanufacturers, and material recyclers (shredders). Today, over 75% of automotive materials, primarily the metals, are profitably recycled via (1) parts reuse and parts and components remanufacturing and (2) ultimately by the scrap processing (shredding) industry. The process by which the scrap processors recover metal scrap from automobiles involves shredding the obsolete automobile hulks, along with other obsolete metal-containing products (such as white goods, industrial scrap, and demolition debris), and recovering the metals from the shredded material. The single largest source of recycled ferrous scrap for the iron and steel industry is obsolete automobiles.
From Argonne National Laboratory report "End-of-Life Vehicle Recycling: State of the Art of Resource Recovery from Shredder Residue"
