As Engels says in the 1883 preface to The Communist Manifesto,

all history has been a history of class struggles, of struggles between exploited and exploiting, between dominated and dominating classes at various stages of social evolution; that this struggle, however, has now reached a stage where the exploited and oppressed class (the proletariat) can no longer emancipate itself from the class which exploits and oppresses it (the bourgeoisie), without at the same time forever freeing the whole of society from exploitation, oppression, class struggles—this basic thought belongs solely and exclusively to Marx.

So class struggle—the struggle between those who labor day-by-day for a living and those who profit from the labor of others because they own the means of production—is the key struggle. This is important because other groups frame the conflict or struggle differently. The fascists, for example, see the universal struggle as not between economic classes, but between races. For example, the Nazis understood all the Aryan people, rich and poor, as united by race against common enemies such as Jews and Slavs. Nationalist ideologies in general understand people of one nation as united together against enemies comprised of an entire other country. For example, the US might say it is at war with "Iraq," not certain forces in Iraq that are hostile to its interests.

One specific example of struggle in The Communist Manifesto would be that of the artisan class, which Marx labels as part of the proletariat. The artisan class rebels against the factory mechanization of its work, which robs the artisan of his autonomy. He will initially fight back to smash the factory, trying to retain his freedom and not become a wage slave.

After industrialization, a group that Marx calls the lumpenproletariat forms: they are the doctors, lawyers and others who have lost prestige and power, who have been converted into wage earners, and some of them become reactionaries, wanting to return to a perceived golden age.

In the first chapter of the Communist Manifesto, Karl Marx writes that the history of struggles is between people of a different class. Specifically, this is a struggle between "the oppressed and the oppressing" and Marx provides several examples: "freeman and slave, patrician and plebeian, lord and serf, guild-master and journeyman." 

If we take one of these examples, like the lord and serf, we can put this into context. In the Middle Ages, a serf was a unfree peasant who lived and worked on his lord's land. Under the system of feudalism, the serf could not leave this land, could not marry without his lord's consent and had to dedicate much of his labour to producing food specifically for his lord's family. This, argues Marx, is an exploitative relationship because the serf is economically subservient to his lord. It is the lord who benefits from this relationship through his control of the means of production (the land) while the serf lives in bondage. 

Historically, feudalism began to decline in the 1400s, brought on by new economic conditions after the Black Death of 1348. As a result, serfdom died out but, according to Marx, the exploitation of workers continued, just under a new name.