There are a few particularly interesting points when you go back up your ancestor tree. First, there is a point where some ancestor of yours is an ancestor of everyone else currently living (and so will also be an ancestor of everyone else to come). This is the "most recent common ancestor" point.

Go farther back and you reach the "identical ancestors point" (also known as the "all common ancestors point" or the "genetic isopoint"). The is the most recent point where everyone alive either is an ancestor of everyone currently living or has no living descendants.

Even farther back is the "Mitochondrial Eve" (or "matrilineal most recent common ancestor"). This is like the "most recent common ancestor" except only counts matrilineal descent. I.e., it is the most recent point where there is a woman that all currently living people can trace their ancestry to entirely through women.

There's a similar point for the "Y-chomosomal Adam" via patrilineal descent.

It is believed that the identical ancestor point is less than 15000 years ago. Note that this is after the Neanderthals went extinct. It follows that since there are people alive today with Neanderthal ancestry, there must have been people alive at the identical ancestor point who had Neanderthal ancestry and who have descendants alive today, and so by the definition of the identical ancestor point everyone alive today is a descendent of all such people. Hence, we can conclude that every current human has Neanderthal ancestry.

Same goes for the Denisovans.

Note that this doesn't mean that everyone today has Neanderthal or Denisovan DNA. We only have enough genes to have genes from all our ancestors back for 15 or so generations. Because of this you can have someone who is an ancestor of yours but you have none of their DNA.