what was the function of the Roman cavalry?

[drsrob]

Col. Ardant du Picq argues that cavalry were ineffective against steady and disciplined ranks of infantry, and he was an actual contemporary of, and witness to, cavalry in battle (9th Chausseurs and the Crimean).

In other periods cavalry did charge steady infantry, often overruning it, and it was trained to do it.

In what periods for instance?