Recent studies have shown that intelligent reflecting surfaces (IRS) can significantly improve the spectral and energy efficiency of wireless communication links. However, most works assume perfect transceivers and IRS, which is impractical in real communication systems. In this work, we study the effect of the hardware impairments in IRS-assisted MISO systems with single user, where we consider both phase noise caused by the imperfect transceivers and IRS. To this end, we propose a linear minimum mean square error (LMMSE) channel estimation algorithm that takes the phase noise into account. Furthermore, we study the impact of phase noise on the downlink performance of an IRS-assisted system. Both analytical and numerical results are presented, where we prove that the transceiver phase noise can be compensated with the optimized IRS, while the IRS phase noise remains but is not exacerbated. As the number of reflective elements $N$ approaches infinity, the IRS phase noise results in a constant loss in terms of the ergodic rate. Moreover, we find that the phase noise has no impact on the scaling laws. If the direct channel is blocked and as $N \rightarrow \infty$ , the transmit power can be scaled down by $\frac {1}{N}$ and $\frac {1}{N^{2}}$ , respectively, for random and optimized IRS, without compromising the received signal to noise ratio (SNR).