Cross-domain sequential recommendation (CDSR) shifts the modeling of user preferences from flat to stereoscopic by integrating and learning interaction information from multiple domains at different granularities (ranging from inter-sequence to intra-sequence and from single-domain to cross-domain). In this survey, we first define the CDSR problem using a four-dimensional tensor and then analyze its multi-type input representations under multidirectional dimensionality reductions. Following that, we provide a systematic overview from both macro and micro views. From a macro view, we abstract the multi-level fusion structures of various models across domains and discuss their bridges for fusion. From a micro view, focusing on the existing models, we first discuss the basic technologies and then explain the auxiliary learning technologies. Finally, we exhibit the available public datasets and the representative experimental results as well as provide some insights into future directions for research in CDSR.