Paper for Organic Compost?

I keep reading and hearing that all waste paper and cardboard can go in the compost bin. A lot of chemicals are used in paper processing to bleach the wood white. Then there is all the inks that go into coloured magazines and packaging etc. Does this really make a healthy compost to grow vegetables on? Are all products used in publishing today biodegradable?

I don't know where you have read those things, but the only paper products that are normally recommended to put on the compost heap are brown cardboard and non-coloured paper.  The reason is, as you say, coloured inks may contain chemicals which are detrimental to the growth of plants or bacteria.

After doing some research, it appears that the heavy metals which used to be used in coloured inks (particularly glossy things) haven't been used for a couple of decades, and current inks are vegetable oil based.  This had to be done to protect workers in printing factories.  So, it does appear that it's safe to compost even coloured paper these days.  Several sites specialising in composting still advise avoiding glossy paper as it contains up to 50% clay (which is what makes it shiney), but that is only because it takes a lot longer to break down.

If you put paper on a compost heap, shred it first as this speeds up the breaking down process.

I shred all of my white paper waste and just put in on my compost heap which is not in a container. If you put very large quantities of paper, cardboard etc on the heap it just compacts down into a solid mass, it does eventually break down but very slowly.