In this talk, I will set up the general Euler system machinery of Rubin and look at its properties and examples.

I will then briefly recall the construction of the Beilinson – Flach Euler system associated to the Rankin – Selberg convolution of a pair of p-ordinary cusp forms (after Bertolini – Darmon – Rotger and Kings – Lei – Loeffler – Zerbes). This will be an expository talk aimed at a general audience.