A tale of two types of Selmer groups for quadratic twists of elliptic curves

We will discuss the statement of Poonen-Rains heuristics, its relation to different approaches employed for number fields and function field settings, and some difficulties in verifying the heuristics. If time allows, we will mention current work in progress on computing the secondary terms for first moments of 2-Selmer groups of quadratic twists of elliptic curves over global function fields.