This paper investigates the impact of non-ideal hardware impairments on the performance of massive MIMO systems. It shows that hardware impairments create finite ceilings on channel estimation accuracy and on the downlink/uplink capacity of each user equipment (UE). Surprisingly, the capacity is mainly limited by the hardware at the UE, while the impact of impairments in the large-scale arrays vanishes asymptotically and inter-user interference becomes negligible. The paper proves that the huge degrees of freedom offered by massive MIMO can be used to reduce the transmit power and/or tolerate larger hardware impairments, which allows for the use of inexpensive and energy-efficient antenna elements. The paper considers a new system model that incorporates general transceiver hardware impairments at both the BSs and the UEs. It derives a new pilot-based channel estimator and shows that the estimation accuracy is limited by the levels of impairments. The paper also derives lower and upper bounds on the downlink and uplink capacities, revealing the existence of finite capacity ceilings due to hardware impairments. Despite these results, the paper shows that high energy efficiency and resilience towards hardware impairments at the BS can be achieved. The paper also puts these results in a multicell context and shows that inter-user interference (including pilot contamination) basically drowns in the distortion noise from hardware impairments. The paper also discusses the impact of various refinements of the system model. The paper concludes that the results show that the use of large-scale antenna arrays can bring substantial improvements in energy and/or spectral efficiency to wireless systems due to the greatly improved spatial resolution and array gain.This paper investigates the impact of non-ideal hardware impairments on the performance of massive MIMO systems. It shows that hardware impairments create finite ceilings on channel estimation accuracy and on the downlink/uplink capacity of each user equipment (UE). Surprisingly, the capacity is mainly limited by the hardware at the UE, while the impact of impairments in the large-scale arrays vanishes asymptotically and inter-user interference becomes negligible. The paper proves that the huge degrees of freedom offered by massive MIMO can be used to reduce the transmit power and/or tolerate larger hardware impairments, which allows for the use of inexpensive and energy-efficient antenna elements. The paper considers a new system model that incorporates general transceiver hardware impairments at both the BSs and the UEs. It derives a new pilot-based channel estimator and shows that the estimation accuracy is limited by the levels of impairments. The paper also derives lower and upper bounds on the downlink and uplink capacities, revealing the existence of finite capacity ceilings due to hardware impairments. Despite these results, the paper shows that high energy efficiency and resilience towards hardware impairments at the BS can be achieved. The paper also puts these results in a multicell context and shows that inter-user interference (including pilot contamination) basically drowns in the distortion noise from hardware impairments. The paper also discusses the impact of various refinements of the system model. The paper concludes that the results show that the use of large-scale antenna arrays can bring substantial improvements in energy and/or spectral efficiency to wireless systems due to the greatly improved spatial resolution and array gain.