Or at least one of them. Blue Origin is a lesser known outfit than Space X, but they're also working on reusing "lower" stages of rockets. But in some ways they're making more progress.
And this weekend they launched a rocket that had been used before for the first time.
Blue Origin is using smaller and less technically complex rockets than Space X, which probably contributes to them being ahead. But they have proved it's absolutely possible to reuse the first stage of a rocket without it blowing up in the second launch.
Their tests should also establish how many times we can reasonably reuse a craft - important data for when we start using these techniques to launch people into space.