Reconfigurable intelligent surface (RIS) can effectively control the wavefront of the impinging signals and has emerged as a cost-effective promising solution to improve the spectrum and energy efficiency of wireless systems. Most existing researches on RIS assume that the hardware operations are perfect. However, both physical transceiver and RIS suffer from inevitable hardware impairments in practice, which can lead to severe system performance degradation and increase the complexity of beamforming optimization. Consequently, the existing researches on RIS, including channel estimation, beamforming optimization, spectrum and energy efficiency analysis, etc., cannot directly apply to the case of hardware impairments. In this paper, by taking hardware impairments into consideration, we conduct the joint transmit and reflect beamforming optimization, and reevaluate the system performance. First, we characterize the closed-form estimators of direct and cascaded channels in both single-user and multi-user cases, and analyze the impact of hardware impairments on channel estimation accuracy. Then, the optimal transmit beamforming solution is derived, and a gradient descent method-based algorithm is also proposed to optimize the reflect beamforming. Moreover, we analyze the three types of asymptotic channel capacities with respect to the transmit power, the antenna number, and the reflecting element number. Finally, in terms of the system energy consumption, we analyze the power scaling law and the energy efficiency. Our experimental results also reveal an encouraging phenomenon that the RIS-assisted wireless system with massive reflecting elements can achieve both high spectrum and energy efficiency without the need for massive antennas and without allocating too many resources to optimize the reflect beamforming.