Liquid-phase epitaxy (LPE) has emerged as the predominant materials growth technology for the fabrication of HgCdTe infrared (IR) detectors in the IR community over the past decade. This paper reviews one of the most successful LPE technologies developed for HgCdTe, specifically, 'infinite-melt' vertical LPE (VLPE) from Hg-rich solutions. A historical perspective and the current status of VLPE technology are reported. Extensive statistics of performance and producibility of the VLPE technology are elaborated to show its maturity and manufacturing readiness. Particular emphasis is placed on the key role of the double-layer heterojunction (DLHJ) detectors realized by the VLPE technology for high-performance second-generation focal plane arrays. Recent developments in the successful use of the VLPE technology for epitaxial growth on Si-based alternative substrates and for growth of triple- layer heterostructures for two-color applications, which further demonstrate the versatility of the technology, are also reported. The review concludes with a discussion of the prospects for use of the VLPE technology for fabricating advanced device structures of high performance as well as investigating fundamental material properties of HgCdTe.