The black death spread throughout Eurasia, peaking from 1347 to 1351 in Europe and recurring regularly after that.

Contemporary Europeans reffered to it as the 'Great Mortality', to Muslims it was 'the Year of Annihilation'. I'll focus my answer on Europe as that's what I'm most familiar with.

Europeans first encounter with the Black Death came at the Genose colony of Caffa on the Crimean peninsular in 1345-6. Initially the Genose rejoiced as they watched the besieging Tartar army struck down by a mysterious desease, which they associated with divine favour.

As the plague spread throughout Europe however attitudes quickly changed. It was widely viewed as a punishment from a wrathful God. For a brief moment in the middle of the fourteenth century, the words of Genesis 7—“All flesh died that moved upon the earth”—seemed about to be realized and people contemplated the end of civilization. In September 1349, the English king Edward III declared that “a just God now visits the sons of men and lashes the world.” This led to a heightened form of religiosity, the flagellants being one example of this.

To many others, the only credible explanation for death on so vast a scale was human malfeasance. Evildoers were using poisons to spread the plague, warned Alfonso of Cordova. To many of Alfonso’s contemporaries, that could only mean one thing. The Great Mortality occasioned the most violent outburst of anti-Semitism in the Middle Ages, a period already marked by violent anti-Semitic outbursts.

Others sought natural explanations for the desease, inspiring a wave of quasi scientific enquiry. Speculation ranged from bad gasses emerging from fissures in the earth, to blaming bad hygiene, particularly the presence of rats!

Source : The Great Mortality by John Kelly