Homogeneous dynamics concerns the study of dynamical properties of a group H acting on a homogeneous space G/S, where G is a Lie group, S is a lattice in G and H is a closed subgroup of G. This area has deep connection with Geometry, Number Theory and Representation Theory. For example, in the number theory some problems about Diophantine approximation have a profound connection with properties of orbit closures in homogeneous dynamics. We will give a rough description of some connections between homogeneous dynamics and number theory, and then introduce some recent works.