how did Marx and Engel's theory of history shape their social and political thought?

Well, both of them were basically talking about "class strugle" in which there is always a "proletariat" who is in antagonism with the "capitalist" and this process would produce a crash of interests: the capital would never know how bad is the life of the proletariat, and will never care about it. So, the only option of the proletariat would be the armed strugle in the form of a revolution that would change the structure of the society and the "distribution of wealth". However, a more complete vision of this is given by Leon Trotsky....I particularily like his point of view, because its less theoretical and more social-practical.

marx and engels realised that all history ran in stages of repression through to rebellion - Marx in his later work actually states that he believed that things would actually have to get much worse in order for the working man to rise up - he also described the various stages until full socialism would or could be attained