Anachronical history is a look at history in which one tries to place that history in the context of what we know now. Conversely, diachronical attempts to take a modern perspective out of the study of history, and to understand historical events within the bounds of their own eras.
Anachronical history is not without it's advantages. For one think, it's almost impossible to study history without at least a tint of a modern viewpoint, and an anachronical history can provide a historian with the means to see an entire chain of progress in a very specific study without it seeming disjointed. However, I think that there are more advantages to a diachronical history, because this seems more realistic, and could allow for a greater understanding as to why certain individuals in the past did what they did. Diachronical history also, as I see it, provides a more complete history, because it includes facts that we might now otherwise consider to be unimportant.
Overall, I think that the past should be viewed with a perspective that is partly anachronical and party diachronical, so one can have the best of both. No matter how we view it, I think that the study of history is and will continue to be indispensable moving forward.