Considerable effort has been devoted to the development of superconducting undulators (SCUs) intended for particle accelerator-based light sources, including synchrotrons and free electron laser (FEL) facilities. Recently, a high-temperature superconducting (HTS) undulator prototype, consisting of staggered-array Re-Ba-Cu–O bulks, achieved an on-axis sinusoidal magnetic field profile with a peak amplitude B₀ of 2.1 T and a period length of 10 mm, resulting in a deflection parameter K = 1.96. Such a short period HTS undulator not only enables the generation of higher-energy photons, but also supports the construction of economically feasible and compact FELs with shorter linear accelerators (LINACs). This article provides a comprehensive review of recent advances in the staggered-array bulk HTS undulator as well as other types of HTS undulators. Furthermore, it offers insights into the development of engineering HTS undulator prototypes designed for deployment in synchrotron and free electron laser (FEL) facilities. We conclude by discussing opportunities for and the challenges facing the use of HTS undulators in practical applications.