Equidistribution results play an important role in dynamical systems and their applications in number theory. Often in such applications it is necessary for equidistribution to be effective (i.e. the rate of convergence is known) so that number-theoretic methods such as sieving can be applied. In this talk, we will give a brief history of effective equidistribution results in homogeneous dynamics and their applications to number theory. We will then present an effective equidistribution result for certain flows on the space of lattices and discuss a number-theoretic application regarding almost-prime times for these flows.