A prominent feature of millimeter wave communications is the blockage effect: an object intruding the line-of-sight (LOS) of a communication link can block the millimeter wave signal. While the blockage incurs outage to the communications, it also brings information related to the blocking object. In this paper, both short-term and long- term trajectory estimations are studied for the object(s) blocking the millimeter wave communication link(s). For the short-term trajectory, experiment has revealed signal strength oscillations before and after the blockage, due to the reflection at the blocking object and the interference with LOS signal. It is shown that the short-term trajectory, as well as the speed, of the moving object can be estimated from the samples of oscillations. For the long-term trajectory, the tracking of multiple objects is carried out using the blockage events on multiple millimeter wave communication links. The trajectory estimation is converted to the problem of object recognition, which is solved by exploiting the geometric intuition. Numerical and experimental results show that the proposed short-term and long-term trajectory estimations achieve excellent performances.