In this thesis for Habilitation à diriger des recherches, we describe our recent work on graph theory and combinatorial game theory. A first chapter is dealing with graph parameters, especially on the structural constraints that permit to give better general bounds. We consider in particular paired domination, independent domination but also cograph partitions and near colorings. In a second chapter, we propose a tentative survey of the known results on power domination, an iterated variation of domination. Finally, the third chapter is about games. We first present our recent results about some conjectures on a domino game, toppling dominoes, and then about misère games. We finally discuss a domination game, which is a graph parameter based on a game.
