If you use any version of the software, please cite the Users Guide:

X.S. Li and J.W. Demmel and J.R. Gilbert and L. Grigori and M. Shao and I. Yamazaki, "SuperLU Users' Guide", Tech report LBNL-44289, Lawrence Berkeley National Laboratory, September 1999 (Last update: June 2018) The following article gives a good overview all three versions: serial, shared-memory, and distributed-memory, with a little more emphasis on users aspects:

X.S. Li, "An Overview of SuperLU: Algorithms, Implementation, and User Interface", ACM Trans. on Math. Software}, Vol. 31, No. 3, September 2005, pp. 302-325.

If you use the GPU versions or the 3D version, please cite the following articles:

Xiaoye S. Li, Paul Lin, Yang Liu, and Piyush Sao. 2023. Newly Released Capabilities in the Distributed-Memory SuperLU Sparse Direct Solver. ACM Trans. Math. Softw. 49, 1, Article 10 (March 2023). https://doi.org/10.1145/3577197
Y. Liu, N. Ding, P. Sao, S. Williams, X.S. Li, Unified Communication Optimization Strategies for Sparse Triangular Solver on CPU and GPU Clusters, SC23, Nov. 2023. doi.acm.org?doi=3581784.3607092
N. Ding, Y. Liu, S. Williams, X.S. Li, A Message-Driven, Multi-GPU Parallel Sparse Triangular Solver, Proc. of SIAM Conf. on Applied and Computational Discrete Algorithm (ACDA21), July 19-21, 2021.
P.Sao, R.Vuduc, X.Li, A communication-avoiding 3D algorithm for sparse LU factorization on heterogeneous systems, J. Parallel and Distributed Computing (JPDC), September 2019. doi: 10.1016/j.jpdc.2019.03.004.

If you use sequential SuperLU, please cite the Users Guide and the following article:

James W. Demmel, Stanley C. Eisenstat, John R. Gilbert, Xiaoye S. Li, and Joseph W. H. Liu, "A Supernodal Approach to Sparse Partial Pivoting", SIAM Journal on Matrix Analysis and Applications, 1999, Volume 20, Issue 3, Pages 720-755. https://doi.org/10.1137/S0895479895291765

If you use ILU routines in SuperLU, please cite the following article:

Xiaoye S. Li and Meiyue Shao. 2011. "A Supernodal Approach to Incomplete LU Factorization with Partial Pivoting". ACM Trans. Math. Softw. 37, 4, Article 43 (February 2011), 20 pages. https://doi.org/10.1145/1916461.1916467

If you use SuperLU_MT (for shared-memory parallel machines), please cite the following article:

James W. Demmel, John R. Gilbert, and Xiaoye S. Li, "An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian Elimination" SIAM Journal on Matrix Analysis and Applications, Vol. 20, Iss. 4 (1999). 10.1137/S0895479897317685

If you use SuperLU_DIST (for distributed-memory parallel machines), please cite the following articles:

Xiaoye S. Li and James W. Demmel. 2003. SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems. ACM Trans. Math. Softw. 29, 2 (June 2003), 110-140. https://doi.org/10.1145/779359.779361
Xiaoye S. Li, Paul Lin, Yang Liu, and Piyush Sao. 2023. Newly Released Capabilities in the Distributed-Memory SuperLU Sparse Direct Solver. ACM Trans. Math. Softw. 49, 1, Article 10 (March 2023). https://doi.org/10.1145/3577197

If you use the parallel symbolic factorization functionality in SuperLU_DIST, please also cite the following article:

Laura Grigori, James W. Demmel, and Xiaoye S. Li, "Parallel Symbolic Factorization for Sparse LU with Static Pivoting", SIAM Journal on Scientific Computing, Vol. 29, Iss. 3 (2007). 10.1137/050638102

If you use the parallel heavy-weight perfect matching for row permutation (numerical pivoting in SuperLU_DIST), please also cite the following article:

Ariful Azad, Aydin Buluç, Xiaoye S. Li, Xinliang Wang, and Johannes Langguth, "A Distributed-Memory Algorithm for Computing a Heavy-Weight Perfect Matching on Bipartite Graphs", SIAM Journal on Scientific Computing, Vol. 42, Iss. 4 (2020). 10.1137/18M1189348