In this talk I will focus on statistics of solvability of conics over the integers and statistics of failure of weak approximation for the solution set. I will discuss recent joint work with Peter Koymans where we established Stevenhagen´s conjecture on the solvability of the negative Pell equation, and joint work in progress with Alex Bartel where we studied the statistics of the reduction modulo a fixed integer of unit groups of varying real quadratic number fields.