These talks provide an introduction to mapping class groups of infinite-type surfaces. In the first talk, we survey basic examples of infinite-type surfaces and then turn to general features of their mapping class groups, emphasizing the interplay between the topology of the mapping class group and its algebraic structure. The second talk focuses on geometric aspects. We first present the general framework of coarsely bounded generation and the resulting large-scale geometry of CB-generated groups, and then illustrate this framework through concrete examples arising from big mapping class groups.