Sixth-generation (6G) wireless communication systems, as stated in the European 6G flagship project Hexa-X, are anticipated to feature the integration of intelligence, communication, sensing, positioning, and computation. An important aspect of this integration is integrated sensing and communication (ISAC), in which the same waveform is used for both systems both sensing and communication, to address the challenge of spectrum scarcity. Recently, the orthogonal time frequency space (OTFS) waveform has been proposed to address OFDM's limitations due to the high Doppler spread in some future wireless communication systems. In this paper, we review existing OTFS waveforms for ISAC systems and provide some insights into future research. Firstly, we introduce the basic principles and a system model of OTFS and provide a foundational understanding of this innovative technology's core concepts and architecture. Subsequently, we present an overview of OTFS-based ISAC system frameworks. We provide a comprehensive review of recent research developments and the current state of the art in the field of OTFS-assisted ISAC systems to gain a thorough understanding of the current landscape and advancements. Furthermore, we perform a thorough comparison between OTFS-enabled ISAC operations and traditional OFDM, highlighting the distinctive advantages of OTFS, especially in high Doppler spread scenarios. Subsequently, we address the primary challenges facing OTFS-based ISAC systems, identifying potential limitations and drawbacks. Then, finally, we suggest future research directions, aiming to inspire further innovation in the 6G wireless communication landscape.