How densely can we pack unit spheres in the d-dimensional space? How many unit spheres can tough a single unit sphere in the d-dimensional space? Both questions are considered by mathematicians for centuries; however, our understanding for both problems is still very limited. In a recent work we show that random configurations, for the first question, meet the current best known lower bound up to a multiplicative constant (asymptotically in the dimension) and for the second question they even give rise to the first improvement since the 1950s. This is joint work with Matthew Jenssen and Will Perkins.