Recently several fundamental works have been done in Geometry of numbers. Beside Bhargava's revolutionary ideas (an of course the contribution of his students), Ergodic theory is a new idea that plays an important role in Modern Geometry of Numbers. It seems to me that several ideas are coming from Margulis and E. Lindenstrauss.
Here are a list of works in this area which I think they are extremely interesting
Minkowski's theorem for random lattices, . Margulis (Russian) Problemy Peredachi Informatsii 47 (2011), no. 4, 104--108; translation in Probl. Inf. Transm. 47 (2011), no. 4, 398–402
Logarithm laws for unipotent flows. I, Athreya; Margulis
On the probability of a random lattice avoiding a large convex set, Strömbergsson
A note on sphere packings in high dimension, Venkatesh
On the distribution of angles between the $N$ shortest vectors in a random lattice, Södergren, Anders
Remarks on Euclidean Minima, Uri Shapira, Zhiren Wang
On the Mordell-Gruber spectrum, Uri Shapira, Barak Weiss
A solution to a problem of Cassels and Diophantine properties of cubic numbers, Uri Shapira
