The unicorn of map projections is the one that preserves all the spatial relationships from the globe. Topologically, we know this projection doesn’t exist, as it is impossible to preserve both areal and angular relationships from the sphere when projected to the flat map, so we make do the best that we can by balancing distortions to areal and angular relationships to suit the needs of specific mapping projects. Balancing these distortions is a challenge that we all face in spatial analytics or cartographic design. However, people don’t tend to like inaccuracies, at least once they have been pointed out to them. Combine this with little to no interest in, or ability to, understand / compensate for map projection distortion, and the lure of a single ‘perfect map’ is strong enough to draw many away from the vital consideration of selecting a specific map projection to match the intended purpose of the map. This paper discusses several map projections that have been introduced in the recent past and noted as being "the world's most accurate" or similar. I discuss these projection unicorns, their characteristics, limitations, and how they may help, or hinder us, in making better maps to understand the world around us. Since the impact of distortion for global-scale mapping is the most challenging, I will focus on what makes maps work (or not), and some solutions, at this scale.