  Generative AI (GenAI) marked a shift from AI being able to recognize to AI
being able to generate solutions for a wide variety of tasks. As the generated
solutions and applications become increasingly more complex and multi-faceted,
novel needs, objectives, and possibilities have emerged for explainability
(XAI). In this work, we elaborate on why XAI has gained importance with the
rise of GenAI and its challenges for explainability research. We also unveil
novel and emerging desiderata that explanations should fulfill, covering
aspects such as verifiability, interactivity, security, and cost. To this end,
we focus on surveying existing works. Furthermore, we provide a taxonomy of
relevant dimensions that allows us to better characterize existing XAI
mechanisms and methods for GenAI. We discuss different avenues to ensure XAI,
from training data to prompting. Our paper offers a short but concise technical
background of GenAI for non-technical readers, focusing on text and images to
better understand novel or adapted XAI techniques for GenAI. However, due to
the vast array of works on GenAI, we decided to forego detailed aspects of XAI
related to evaluation and usage of explanations. As such, the manuscript
interests both technically oriented people and other disciplines, such as
social scientists and information systems researchers. Our research roadmap
provides more than ten directions for future investigation.
