It is commonly assumed that the litis aestimatio of the actio legis Aquiliae was a penalty which, in practice, was set at the loss suffered by the victim of the wrong and therefore functioned as compensation. This assumption is based on the nature of the action as founding in a delict and characterised by the Romans as a penal action. It also shares the elements of penal actions. But this is at odds with other texts which treat the action as directed purely at compensation. It is suggested that in order to understand this we have to distinguish between the origin of the penal actions, which is penal and which carries certain common features such as the fundamental impossibility to sue heirs or descendants of the wrongdoer, and their purpose or object. It is possible to distinguish two groups, one aiming at a penalty, the other aiming at compensation. Only in the latter group the action can be exercised against the heir of the wrongdoer and only restrictedly: it is the compensatory aim which allows for this. Further, the lex Aquilia and its chapters are examined whether a compensatory purpose is distinguishable here as well.