High-Tc superconducting (HTS) flux pumps are capable of injecting flux into closed HTS magnets without electrical contact. It is becoming a promising alternative of current source in powering HTS coils. This paper reviews the recent progress in flux pumps for HTS coil magnets. Different types of HTS flux pumps are introduced. The physics of these flux pumps are explained and comparisons are made.J. Geng would like to acknowledge Cambridge Trust for offering Cambridge International Scholarship to support his study in Cambridge