In the case of Roman history it's the First Punic War talked about in the "Bellum Punic" of Gnaeus Nevius (who fought in the war). The work is basically lost but we have some fragments and it was used by later annalists I think.
The most interesting is the greek historian Polybius who was present at the destruction of Carthage in 146 BC. He mentions that Scipio Aemilianus was kind of sad. Polybius asked Scipio why and he said: "Troy fell, Carthage is falling, one day Rome will fall too".
Another author who was an interesting eyewitness is Pliny the Younger regarding the eruption of Mount Vesuvius.