Only recently the focus in numerical cognition research has considered multi-digit number processing as a relatively new and yet understudied domain in mathematical cognition. In this chapter: we argue that single-digit number processing is not sufficient to understand multi-digit number processing; provide an overview on which representations and effects have been investigated for multi-digit numbers; suggest a conceptual distinction between place-identification, place-value activation, and place-value computation; identify language influences on multi-digit number processing along that conceptual distinction; and argue that for (...) numerical development indices of multi-digit number processing may be more suitable predictors of later arithmetical performance than classical single-digit measure such as the distance effect or non-numerical variables. In the final section, we summarize the important issues in multi-digit number processing, outline future directions and try to encourage readers to contribute to a new, exciting, yet understudied domain of numerical cognition. (shrink)