How many perfect squares have a value between 10 and 1000?
We can see that $3^2 = 9 < 10 < 4^2 = 16$. Thus, $4^2 = 16$ is the smallest perfect square between 10 and 1000.

We also see that $31^2 = 961 < 1000 < 32^2 = 1024$. Thus, $31^2 = 961$ is the greatest perfect square between 10 and 1000.

It follows that there are $31 - 4 + 1 = \boxed{28}$ perfect squares between 10 and 1000.