Before 64 AD there was no real organized persecution of Christians -- at least throughout the empire -- that does not mean that there was no persecution nor does it mean that there were few who suffered. It only means that the majority of the persecution was born of Jewish hostility to Christianity and local in nature. Certainly after the great fire (64 AD), Nero undertook a persecution of Christians.
From then to 250 AD, there were many isolated persecutions, again not necessarily empire wide, but it was definitely on the upsweep. Even if the actual number of victims was greater, it does not yet mean that the persecution of victims was uniform practice and across the scope of the empire.
From 250 to 313 AD, there were more general times of persecution of Christians, usually lasting a year to three years in length and often more in the East than in the West.
Christians proved to be convenient scapegoats. Once the first batch of Nero's victims had been marked for persecution, it was easier to bring the charge of simply being a Christian against someone. Christianity became then, by definition, an anti-social and potentially criminal conspiracy.
From about 112 or so oneward, Christians began to be punished for the nomen Christianum. We find this in some of the early Christian apologists, in some of the martyrdoms, and from exchanges of official letters. Pliny speaks of Christians he had executed for being Christian. Trajan is careful not to order that Christians be sought out or that anonymous evidence be sufficient against them but does suggest that Christians could prove their innocence by offering up prayers to the Roman gods.
Roman law was among the most impressive achievements of the whole of Roman civilization. It was, however, mostly private law protecting and defining such things as property rights. Criminal law was not quite so impressive. The magistrates had wide latitude here not only for dispensing punishment but even for defining what was criminal.
Though it was often common to distinguish between good emperors and bad emperors (those who did not and those who did persecute Christians), persecution was not limited to a few personalities. That said persecutions usually awaited someone to bring charges and local governors were hardly resistant to public sentiment when it arose against Christians.
Christians were often charged with crimes that the general public would find most objectionable (like cannibalism and incest). By the end of the second and well into the third centuries, Christian apologists had done an effective enough job refuting these charges made this slander hard to prove.
Strange as it may seem to us today, Christians often seemed to volunteer for martyrdom. So much so that church leaders had to write strenuous objections to an astonishingly large number of folks who willingly pursued martyrdom.
Strangely, it was hardly the positive beliefs and practices of Christians which aroused hostility but the refusal of Christians to worship any god but their own, to participate in the civic rites of pagan deities, to pay temple taxes, and to fulfill the good citizenship of Roman which included ensuring a right relationship between their gods and men. Christians openly asserted that the pagan gods either did not exist at all or they were manifestations of the demonic. To Romans in which a civil religion was important for more reasons than for piety, this bordered on treason.
The Decian persecution saw the beginnings of a change. Perhaps it was the fact that Christians had multiplied in number or that pagans had gotten to know Christians differently or the fact that Christianity had outgrown its once jealously guarded secret rites and character. Even in time of persecution, Christians were not charged for private rites or worship of the Triune God but for the failure of their public support of the civil religion of Rome.
Now as we face a modern age, I wonder if the same is not also true. Christians are not under threat for what they do in private but for their failure to acknowledge and support the public religion of the state, the politically correct positions regarding the great issues of the day, and for their refusal to play nice in public and then do what they please in private. It is an attack not essentially against dogma but against patriotism -- certain things must be supported in the name of the nation and all that the nation deems is just, right, and worthy. Christians will probably not ever be attacked behind the closed doors of the worship service but they can be isolated and banished from the public square for their refusal to be good citizens, to abide by laws they deem to be wrong, or to keep their religion private. For some this may not be a great threat, since they have abdicated Christian truth to social justice and advocacy of all that is popular and trendy. For others this is the death knell for the faith. We cannot be one thing in private and another in public -- not as individual Christians who work in the marketplace and live on the public square and not as churches who claim to be beacon's of the eternal light of Christ to a world in darkness.
In other words, we need to pay more attention to the persecutions of Christians in the early years of Christianity because they may signal what is ahead of those who intend to be faithful in public as well as in private.