High gradient magnetic separation (HGMS) is effective in concentrating or removing weakly magnetic particles from slurry and has been applied in many scientific and industrial fields. The basic principles behind HGMS are of great importance to appreciate the effectiveness of HGMS and have received considerable research attention. Modeling of particle capture by matrices provides very intuitive understanding of the HGMS process and models are being used in many experimental and industrial cases to estimate the performance. This review focuses on the modeling of capture of micrometer-sized particles by ferromagnetic matrices in HGMS. Particle capture models of a variety of matrices under different circumstances in three configurations of HGMS are reviewed and presented. Typical particle trajectories around matrices and particle capture efficiency are demonstrated and discussed. (C) 2019 Elsevier B.V. All rights reserved.