The basis of Scientific Socialism, as described by Karl Marx and Friedrich Engels in Communist Manifesto, talks about the abolition of bourgeois' private property (factories, corporations, etc), which in turn will become public. This derives from Marx's Theory of Value, which proposes that the earnings of the capitalist come from the surplass value, extracted by the worker (i.e. the capitalist uses labor-power but pays not for the full amount and thats how he gains profit).
All property relations in the past have continually been subject to
historical change consequent upon the change in historical
conditions.The French Revolution, for example, abolished feudal
property in favour of bourgeois property. The distinguishing feature
of Communism is not the abolition of property generally, but the
abolition of bourgeois property. But modern bourgeois private
property is the final and most complete expression of the system of
producing and appropriating products, that is based on class
antagonisms, on the exploitation of the many by the few. In this
sense, the theory of the Communists may be summed up in the single
sentence: Abolition of private property. We Communists have been
reproached with the desire of abolishing the right of personally
acquiring property as the fruit of a man’s own labour, which property
is alleged to be the groundwork of all personal freedom, activity and
independence. Hard-won, self-acquired, self-earned property! Do you
mean the property of petty artisan and of the small peasant, a form of
property that preceded the bourgeois form? There is no need to abolish
that; the development of industry has to a great extent already
destroyed it, and is still destroying it daily. Or do you mean the
modern bourgeois private property?
Source: Communist Manifesto Chapter II
Btw, I would suggest editing to "What happens with private property in Communism" in order not to be marked as opinion-based.
Edit (motivated by user4012's comment):
the development of industry has to a great extent already destroyed it
Marx's insight here concerned the (violent) expropriation of peasants from their lands by the people who formed the capitalist class afterwards, during the transition from feudal to capitalistic model of economy. The peasants turned into factory workers during industrialization. (Source: Marx's Das Capital, Vol I, On Primitive Accumulation).
and is still destroying it daily.
Even the recent crisis originated from house loans and resulted in millions of homeless people around the globe.