SYM-ILDL is a numerical software package that computes incomplete LDLT (ILDL) factorizations of symmetric indefinite and real skew-symmetric matrices. The core of the algorithm is a Crout variant of incomplete LU (ILU), originally introduced and implemented for symmetric matrices by Li and Saad [2005]. Our code is economical in terms of storage, and it deals with real skew-symmetric matrices as well as symmetric ones. The package is written in C++ and is templated, is open source, and includes a Matlab™ interface. The code includes built-in RCM and AMD reordering, two equilibration strategies, threshold Bunch-Kaufman pivoting, and rook pivoting, as well as a wrapper to MC64, a popular matching-based equilibration and reordering algorithm. We also include two built-in iterative solvers: SQMR, preconditioned with ILDL, and MINRES, preconditioned with a symmetric positive definite preconditioner based on the ILDL factorization.