Many of the other answers already cover most of what I wanted to say, but there's a few points I wanted to add here.
The first would depend on your definition of "no metals" would be. Imagine a world where metals of any sort were extremely rare, life as we know it would be completely different assuming it could still function on the scale that we know. First is that our entire planet would likely behave differently since its magnetic field would either be missing or weak.
However what if we instead said that metal exists, but aside from going very deep, it only exists in tiny amounts. That way we could account for the metals needed to sustain life, as well as other important factors that keep our planet in check. There are many areas around the world where metal just doesn't exist in abundance near the surface that you could model off of.
One interesting twist would be to have a rather abundant sources of a couple different metals that we would consider rare. For example, having just gold means you could eventually have computers however it wouldn't be nearly strong enough to work as armor or weapons. Without effective metals to sink heat, computer would also then be limited to their overall heat output so high-powered applications are out of the picture. There would also be no magnets due to the lack of iron, so things such as a motor are out of the picture.
Another thing is concrete. 561
You don't need metals to work concrete, and it technically doesn't need reinforcement. The Romans even found that by adding volcanic ash to their mixture, their concrete stands up to the erosion of water fairly well. Of course, without reinforcements the concrete will have some major issues to contend with. First thing is that concrete will completely fail when bending, making tall structure at a high risk to high winds and possible earth quakes. It will also take a lot more concrete to make a given structure stable. Pillars have to be large and wide to make up for the lack of metal reinforcements, and according to this article it would have to be about 5 times larger to be around as effective as concrete with steel reinforcements, but would still be susceptible to the bending issue.
Also let's not forget the potential for rubber, as it technically derives from a tree. It can also be processed without the use of metals. The weak side to this is that you would specifically need a climate which could support the growth of rubber trees, assuming the changes in available metals still allows the evolutionary process that would produce rubber trees. However rubber has many great uses that would aid in this society, but it wouldn't necessary replace any of the uses of metal. 308