We survey recent and old upper bounds on the maximum likelihood decoding error probability of linear codes over fading channels. In particular, independent fading with channel state information, receivers with multiple antennas, and receivers with mismatched decoding are considered. The final derived simple bounds do not require integrations. These bounds are the extension of simple bounds derived by Sason-Shamai-Divsalar, and Divsalar-Biglieri for linear codes over independent fading channels. The proposed bounds require only knowledge of the average weight enumerator of the code ensemble for modern codes. The bounds are tight for large block lengths and predict the performance beyond the cutoff rate of the channel.