Deep clustering enables uncovering hidden patterns and groups in complex time series data. Yet, its opaque decision-making limits use in safety-critical settings. This review survey offers a structured overview of explainable deep clustering for time series, collecting current methods and their real-world applications. We discuss and compare peer-reviewed and preprint papers through application domains across healthcare, finance, IoT, and climate science. Our analysis reveals that most work relies on autoencoder and attention architectures, with limited support for streaming, irregularly sampled, or privacy-preserved series, and interpretability is still primarily treated as an add-on and not a goal. To push the field forward, we outline six research opportunities: (1) combining complex networks with built-in interpretability; (2) setting up clear, faithfulness-focused evaluation metrics for unsupervised explanations; (3) building explainers that scale to large data and adapt to live data streams; (4) crafting explanations tailored to specific domains; (5) adding human-in-the-loop methods that refine clusters and explanations together; and (6) improving our understanding of how time series clustering models work internally. By making interpretability a primary design goal rather than an afterthought, we propose the groundwork for the next generation of trustworthy deep clustering time series analytics.