Shtukas?$\mbox{}$ Does there exist an exposition of the significance of _shtukas_ for someone who is mathematically literate but is largelly ignorant of Drinfeld modules? This arises in the work of Peter Scholze among others. Is this notion accessible only to those already immersed in the Langlands conjectures?

The article "What is ... a shtuka?" by David Goss might be helpful. My memory is that the Mumford article cited by Goss is also quite helpful, and (among other things) sheds light on why the person who invented Shtuka's (Drinfeld) also contributed fundamentally to the theory of integrable systems.

For the relationship with Langlands, it helps first to understand modular curves (i.e. moduli spaces of elliptic curves) and their relationship to Langlands for $GL_2$ over $\mathbb Q$. Drinfeld modules, and Shtukas, were introduced by Drinfeld to obtain moduli spaces which could play an analogous role in characteristic $p$. Unfortunately I'm not sure where to go to find an introductory discussion of these analogies. Hopefully someone else will (and I would certainly try asking on MO if no-one here can point you to one).