We consider the problem of recovering an unknown planted matching between a set of $n$ randomly placed points in \mathbb{R}^d and random perturbations of these points. Some recent works have established results for the error rates for this problem under Gaussian assumptions for both initial positions and noise at different scaling regimes of sample size and dimension. I will discuss some recent progress on establishing results which hold under general distributional assumption for both the the initial positions and noise. More precisely, I will show a general recipe to establish lower bounds via showing the existence of large matchings in random geometric graphs, which leads to simplified and generalized proofs of previous results. Time allowing I will also make some remarks regarding sufficient conditions for perfect recovery in high-dimensions for models where the noise is not isotropic. This is joint work with Roberto Oliveira.