A very good but also very simple answer has been given already. In capitalist society, the means of production (machinery, raw materials, etc.) are owned by the bourgeoisie. This is made very explicit in The Communist Manifesto (and most of the rest of what I will say is at least hinted at in there as well).
To give a more complete answer, we should consider that
Marx theorizes the historical development of societies through his concept of modes of production. Each mode of production is essentially defined by how the means of production are controlled. So the answer to your question really depends on which mode of production you have in mind.
In primitive communism, which refers to "tribal" societies or what we might call hunter-gather societies, the means of production are very limited and held in common. There is no ruling class, so the means of production belongs to more or less equally to everyone in the society.
The Asiatic mode of production describes most ancient empires and civilizations. It was the relevant ruling political/priestly class or imperial dynasty that controlled most of the land, the irrigation systems, etc. In short, the means of production was owned by the state.
In Europe and Japan, a feudal system emerged prior to capitalism. This is not fundamentally different from the Asiatic mode, but the state was highly fragmented, de-centralized and divided. Feudal lords therefore had the most direct control over the means of production.
Out of feudalism, a bourgeoisie emerged and gradually took control over the means of production by instituting private property. Feudal lords lost control over the peasants, who became proletarians. This produces the eventual possibility of a pure form of communism, in which control of the means of production would again return to everyone. (Which mode of production best describes the so-called communism in the USSR, China, etc. is debated. Many Marxists see it as a form of capitalism or the Asiatic mode.)
Finally, your question raises the concept of a rentier class. Marx would consider some of the bourgeoisie, like bankers and real estate speculators, to be rentiers. They don't directly own means of production like factories, but they indirectly derive surplus from those means. While elites in non-capitalist societies (feudal lords and other ruling classes) can also be seen rentiers, the concept is more meaningful in the context of capitalist society. It distinguishes what Marx sees as the "non-productive" groups within the bourgeoisie.