Video segmentation encompasses a wide range of categories of problem formulation, e.g., object, scene, actor-action and multimodal video segmentation, for delineating task-specific scene components with pixel-level masks. Recently, approaches in this research area shifted from concentrating on ConvNet-based to transformer-based models. In addition, various interpretability approaches have appeared for transformer models and video temporal dynamics, motivated by the growing interest in basic scientific understanding, model diagnostics and societal implications of real-world deployment. Previous surveys mainly focused on ConvNet models on a subset of video segmentation tasks or transformers for classification tasks. Moreover, component-wise discussion of transformer-based video segmentation models has not yet received due focus. In addition, previous reviews of interpretability methods focused on transformers for classification, while analysis of video temporal dynamics modelling capabilities of video models received less attention. In this survey, we address the above with a thorough discussion of various categories of video segmentation, a component-wise discussion of the state-of-the-art transformer-based models, and a review of related interpretability methods. We first present an introduction to the different video segmentation task categories, their objectives, specific challenges and benchmark datasets. Next, we provide a component-wise review of recent transformer-based models and document the state of the art on different video segmentation tasks. Subsequently, we discuss post-hoc and ante-hoc interpretability methods for transformer models and interpretability methods for understanding the role of the temporal dimension in video models. Finally, we conclude our discussion with future research directions.