The article provides a survey of ideas and initiatives advanced by Christian and Muslim religious leaders and believers towards a mutual religious rapprochement in the past more than fifty years. On the Christian side, the process was started at the Second Vatican Council and developed with the great personal involvement of all popes of the following half-century. Muslim positive initiatives, from official centres as well as from committed intellectuals, have appeared somewhat later and still have to combat hostile moves of partisans of radical Islamism. Our article discusses the culminating point reached so far in the positive efforts of Pope Francis in his meetings with the Grand Imam of Al-Azhar Sheikh Ahmad al-Tayyib, including their agreement on the fraternity as a desirable bond for all believers in God. Our reflections try to mark out the main points of understanding achieved by the two religious leaders in the document signed by them in Abu Dhabi in February 2019 and, thereafter, further developed by the Pope in his comprehensive encyclical Fratelli tutti, issued in Vatican on the feast of Saint Francis in October 2020.