It has one major weakness - it cannot resist tension. So it is superb for arches, but no good for beams. There is a solution to this problem - design the structure so that tension cannot occur in the concrete. This is done by placing steel wires, which are under tension, inside the material to compress the parts that would otherwise be in tension. This is called pre-stressing.
Allowance has to made made for creep, in setting the tension.
The tension needs to be such that under maximum design load, the concrete is never stretched past its original length. Let's go back in time, to the ancient Romans, who discovered how to make and use concrete, and could even make it work under water. But the weakness of concrete in tension meant that it was only useful in masses like walls, or in compression, as in arches. Eventually, when strong metals were available, it became possible to reinforce concrete with iron or steel rods. In 1808, for example, Richard Dodds took out a patent for reinforced concrete.