Here are some papers I’ve seen on the arXiv today that sound interesting:

- Schapira and Schneiders, Derived category of filtered objects
- Frenkel and Teleman, Geometric Langlands Correspondence Near Opers
- Chen and Zhu, Non-abelian Hodge theory for algebraic curves over characteristic p
- Nadler, Cyclic symmetries of A_n-quiver representations
- Furber and Jacobs,

Towards a Categorical Account of Conditional Probability - Ben-Zvi and Nadler, Nonlinear Traces
- Ben-Zvi and Nadler, Secondary Traces
- Steinberg, Topological dynamics and recognition of languages
- Kharlampovich, Mohajeri, Taam, and Vdovina, Quadratic Equations in Hyperbolic Groups are NP-complete
- Berrick and Hesselholt, Topological Hochschild homology and the Bass trace conjecture

And as for something that has been out for a couple of years but definitely worth looking at if you’re interested in derived functors in the sense of Quillen and generalisations is E. Riehl’s book Categorical Homotopy Theory, which complements the existing introduction to model categories very nicely.