Modern astroparticle physics is becoming a high precision science, both from the perspectives of experimental data and observations, as well as with regards to modelling. We are entering a regime, however, where it is technically challenging to make complete use of the highest quality data and simulation techniques. This is a result of some combination of simulation complexity, intractable statistics problems for complex observations, or the poor scalability of classic analysis methods to situations with hundreds or thousands of parameters. In this talk, I will try and present some of the options that are available to us, and argue that simulation based inference (SBI) techniques are a promising avenue. After a more general discussion of the core ideas of SBI, I will discuss gravitational waves and stellar streams as two concrete examples to highlight the sort of challenges we can overcome with these methods in a bid to move beyond the current state-of-the-art.