Optical trapping is widely used in different areas, ranging from biomedical applications, to physics and material sciences. In recent years, optical fiber tweezers have attracted significant attention in the field of optical trapping due to their flexible manipulation, compact structure, and easy fabrication. As a versatile tool for optical trapping and manipulation, optical fiber tweezers can be used to trap, manipulate, arrange, and assemble tiny objects. Here, we review the optical fiber tweezers-based trapping and manipulation, including dual fiber tweezers for trapping and manipulation, single fiber tweezers for trapping and single cell analysis, optical fiber tweezers for cell assembly, structured optical fiber for enhanced trapping and manipulation, subwavelength optical fiber wire for evanescent fields-based trapping and delivery, and photothermal trapping, assembly, and manipulation.