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Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
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What are the tricks for computing/estimating Gromov-Hausdorff distance?
Not sure if this is a helpful example but if $Y$ is the space of a single point, then
$d_{GH}(X,Y) \leq \text{rad} \: X = \inf_{y \in X} \sup_{x \in X} d(x,y),$
which is just the radius of the smalles …