This article surveys the Variable Autonomy (VA) robotics literature that considers two contributory elements to Trustworthy AI: transparency and explainability. These elements should play a crucial role when designing and adopting robotic systems, especially in VA where poor or untimely adjustments of the system's level of autonomy can lead to errors, control conflicts, user frustration, and ultimate disuse of the system. Despite this need, transparency and explainability is, to the best of our knowledge, mostly overlooked in VA robotics literature or is not considered explicitly. In this article, we aim to present and examine the most recent contributions to the VA literature concerning transparency and explainability. In addition, we propose a way of thinking about VA by breaking these two concepts down based on: the mission of the human-robot team; who the stakeholder is; what needs to be made transparent or explained; why they need it; and how it can be achieved. Last, we provide insights and propose ways to move VA research forward. Our goal with this article is to raise awareness and inter-community discussions among the Trustworthy AI and the VA robotics communities.