Summarizing long pieces of text is a principal task in natural language processing with Machine Learning-based text generation models such as Large Language Models (LLM) being particularly suited to it. Yet these models are often used as black-boxes, making them hard to interpret and debug. This has led to calls by practitioners and regulatory bodies to improve the explainability of such models as they find ever more practical use. In this survey, we present a dual-perspective review of the intersection between explainability and summarization by reviewing the current state of explainable text summarization and also highlighting how summarization techniques are effectively employed to improve explanations.