In the 6G era, space-air-Ground integrated networks (SAGIN) are anticipated to deliver global coverage, necessitating support for a diverse array of emerging applications in high-mobility, hostile environments. Under such conditions, conventional orthogonal frequency division multiplexing (OFDM) modulation, widely employed in cellular and Wi-Fi communication systems, experiences performance degradation due to significant Doppler shifts. To overcome this obstacle, a novel two-dimensional (2D) modulation approach, namely orthogonal time frequency space (OTFS), has emerged as a key enabler for future high-mobility use cases. Distinctively, OTFS modulates information within the delay-Doppler (DD) domain, as opposed to the time-frequency (TF) domain utilized by OFDM. This offers advantages such as Doppler and delay resilience, reduced signaling latency, a lower peak-to-average ratio (PAPR), and a reduced-complexity implementation. Recent studies further indicate that the direct interplay between information and the physical world in the DD domain positions OTFS as a promising waveform for achieving integrated sensing and communications (ISAC). In this article, we present an in-depth review of OTFS technology in the context of the 6G era, encompassing fundamentals, recent advancements, and future directions. Our objective is to provide a valuable resource for researchers engaged in the field of OTFS.