What happened to the flood?
At the end of the Halo 3 campaign, Master Chief destroys the ring while he is on it, during which much of the flood died. However, I find it hard to believe that 100% of the flood population was on the ring when it blew up, yet the flood is never mentioned again. If the flood is an infection, then it just needs a little bit of itself to survive for it to start infecting hosts again.
What happened to the flood after Halo 3?
Within lore, nothing has happened with the Flood post Halo 3. With one minor exception. Halo 4 does contain a play mode feature "Flood" enemies where you can play as Flood. But that counts as a simulation in the lore, not actual story. Additionally, some Spartan IV's were sent to find some on Installation 03, but nothing is known to have been found.
That said, the Flood will likely creep up again. They are, in lore, extremely difficult to destroy, and that's why the Forerunners preserved them on the Halo rings. But for now, there is no signs of them.