Episode four began with the rise of the non-Julian emperors--those who were NOT descended from Julius and Augustus Caesar. Now, in their place, came Generals who became leader of the empire simply by destroying all their competition! This pattern would continue, more or less, for the next three plus centuries. And, for the most part, Vespasian was one of the empire's better leaders--though he, also, made the mistake of trying to start a dynasty.
Much of the show also concerned Pliny (the Elder and Younger)--their lives and how they both faired with the destruction of Pompeii. Additional topics were a continuation of a discussion of Josephus, the destruction of Judea, the gladiators and, finally, a brief discussion of the last emperor in the series, Trajan. Unlike Vespasian, Trajan promoted the idea that his successor should be chosen--not simply because of their bloodline.
Like all the other episodes, this one is marvelously made. However, it should be noted that it did NOT end at 101AD (the end of the first century), as the 'Century' in the title was only an approximation.