Meir–Keeler contraction presents an interesting and widely studied topic in the area of Metric Fixed Point Theory. We intend to present several results concerning common fixed problem and the impact of Meir-Keeler-type contractions on this type of results. We will present results on common fixed problem for a Meir–Keeler contraction mapping in various settings—metric space, b-metric space, partial metric space, Branciari metric space, etc. It is our intention to present a comprehensive study on this topic that will present a good starting point for the researchers in the Fixed Point Theory.