The extreme laser intensities reached by current and next generation Petawatt-Class Laser systems open exciting possibilities not only for a number of well-established applications, such as particle acceleration and radiation sources but also for exploring new frontiers reaching into the QED realm. These opportunities also present an outstanding challenge not only for experimental and theoretical science but also for numerical simulations. Fully relativistic particle-in-cell codes such as OSIRIS [1] have established themselves as the tool of choice for modeling these scenarios, but the problems being addressed require efficient use of the largest supercomputing systems available, as well as new algorithms and physics models. In this talk, I will present an overview of the major challenges being addressed in this field. I address the deployment of the PIC algorithm on the latest architectures and ensuring good parallel scalability. I will also discuss reduced models being used for long-scale laser-plasma interaction, and the new physics models and algorithms being introduced to deal with the extreme intensities involved. I will also present novel numerical diagnostics being implemented to analyze the short wavelength radiation generated by charged particles in these high-intensity fields, and the use of machine learning based algorithms for the optimization of laser-plasma accelerator design. [1] R. A. Fonseca et al., Lect Note Comp Sci, vol. 2331, pp. 342-351, (2002)

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