What are the criteria for belonging to a same species?

There is no single definition to determine what makes one same or different species, but the best one that is offered is when the members of the population are reproductively isolated from other organisms and are capable of producing a fertile offspring. If these two criteria are met, they are generally considered to be the same species.

Of course, there are a number of problems associated with this, since it doesn't take into account asexual organisms, fertile hybrids, and any extinct organisms.