Once they're done gassing, Big Boss informs Snake that he himself is not long for this world, as the new strain of the FOXDIE ...

The Metal Gear Solid games span across decades, though not in chronological order. This should clear the timeline up.

Metal Gear Solid 5 ended with the revelation that you hadn’t been playing as Big Boss, but as a man who had been brainwashed and surgically altered to think and look like he was Big Boss.

Metal Gear Solid Delta Snake Eater is coming soon, a new trailer reveals when, and the threats that the original Snake must face.