Subcarrier intensity modulation with direct detection is a modulation/detection technique for optical wireless communication systems, where a pre-modulated and properly biased radio frequency signal is modulated on the intensity of the optical carrier. The most important benefits of subcarrier intensity modulation are as follows: 1) it does not provide irreducible error floor like the conventional on-off keying intensity modulation with a fixed detection threshold; 2) it provides improved spectral efficiency and supports higher order modulation schemes; and 3) it has much less implementation complexity compared to coherent optical wireless communications with heterodyne or homodyne detection. In this paper, we present an up-to-date review of subcarrier intensity modulated optical wireless communication systems. We survey the error rate and outage performance of subcarrier intensity modulations in the atmospheric turbulence channels considering different modulation and coding schemes. We also explore different contemporary atmospheric turbulence fading mitigation solutions that can be employed for subcarrier intensity modulation. These solutions include diversity combining, adaptive transmission, relay assisted transmission, multiple-subcarrier intensity modulations, and optical orthogonal frequency division multiplexing. Moreover, we review the performance of subcarrier intensity modulations due to the pointing error and synchronization error.