  We establish dispersive and Strichartz estimates for solutions to the linear
time-dependent Schr\"odinger equations with potential in three dimensions. Our
main focus is on the small rough time-dependent potentials. Examples of such
potentials are of the form $V(t,x)=T(t) V_0(x)$, where $T$ is quasiperiodic in
time and $V_0$ is essentially an $L^{3/2}$ function of the spatial variables.
We also prove the dispersive estimates for small time-independent potentials
which belong to the interestion of the Rollnik and global Kato classes.
Finally, we settle the question posed by Journe, Soffer, Sogge concerning
Strichartz estimates for potentials that decay faster than $|x|^{-2}$.
