The QR Decomposition (QRD) of communication channel matrices is a fundamental prerequisite to several detection schemes in Multiple-Input Multiple-Output (MIMO) communication systems. Herein, the main feature of the QRD is to transform the non-causal system into a causal system, where consequently efficient detection algorithms based on the Successive Interference Cancellation (SIC) or Sphere Decoder (SD) become possible. Also, QRD can be used as a light but efficient antenna selection scheme. In this paper, we address the study of the QRD methods and compare their efficiency in terms of computational complexity and error rate performance. Moreover, a particular attention is paid to the parallelism of the QRD algorithms since it reduces the latency of the matrix factorization.