Radio frequency energy harvesting (RFEH) and wireless power transmission (WPT) are two emerging alternative energy technologies that have the potential to offer wireless energy delivery in the future. One of the key components of RFEH or WPT system is the receiving antenna. The receiving antenna’s performance has a considerable impact on the power delivery capability of an RFEH or WPT system. This paper provides a well-rounded review of recent advancements of receiving antennas for RFEH and WPT. Antennas discussed in this paper are categorized as low-profile antennas, multi-band antennas, circularly polarized antennas, and array antennas. A number of contemporary antennas from each category are presented, compared, and discussed with particular emphasis on design approach and performance. Current design and fabrication challenges, future development, open research issues of the antennas and visions for RFEH and WPT are also discussed in this review.