Near-field (NF) integrated sensing and communication (ISAC) has the potential to revolutionize future wireless networks. It enables simultaneous communication and sensing operations on the same radio frequency (RF) resources using a shared hardware platform, maximizing resource utilization. NF-ISAC systems can improve communication and sensing performance compared to traditional far-field (FF) ISAC systems by employing the unique propagation characteristics of NF spherical waves with an additional distance dimension. Despite its potential, the NF-ISAC literature covers just a few specialized topics. A comprehensive survey encompassing all aspects of NF-ISAC systems has thus far been lacking. To this end, this paper systematically explores the prodigious potential of NF-ISAC technology. Specifically, an in-depth analysis of both NF and FF systems is provided, investigating their applicability in communication and sensing scenarios. Various channel model scenarios for NF and FF are discussed, emphasizing their distinguishing features. The advantages and philosophies of ISAC are further explored, opening opportunities to investigate both narrow-band and wide-band systems within NF ISAC. Case studies and simulation examples for each NF-ISAC design philosophy are provided to gain deeper insights into these system designs. An extensive literature review of existing NF-ISAC studies is conducted, exploring various methodologies, potentials, prospects, and conclusions. Finally, prospective research areas, remaining challenges, and applications of future NF-ISAC systems are discussed.