In their 1994 paper, G. Ivanoff and E. Merzbach introduced the notion of a set-indexed strong submartingale, a generalization of the planar strong submartingales defined in the 1975 paper of R. Cairoli and J. Walsh.

After motivating their definition through simple examples, we will present several results in the theory of set-indexed strong submartingales including:

- A Doob-Meyer-type decomposition.

- The definition and existence of quadratic variation for square integrable set-indexed strong martingales.

- The role of set-indexed strong martingales in a Levy-type characterization of set-indexed Brownian motion.

Time permitting, the framework for strong martingale central limit theorems will be discussed.