A survey of several different parameters that measure how complicated a graph is, e.g. tree-width, path-width, clique-width, rank-width, twin-width, etc. There are rough min-max theorems for some of them (e.g. graphs have big tree-width if and only if they contain a large grid as a minor), and we cover some of these. In addition, we cover some associated algorithms (can we test if G has path-width at most 100 in polynomial time?), and some of the ways to use if one of these parameters is bounded. We may briefly stray into the theory of well-quasi-ordering.