Materialism is older than most people assume. Democritus argued in the fifth century BCE that reality consists of atoms and void, and Epicurus built an entire ethics on that foundation — including the argument that death is nothing to us, since when the atoms composing us disperse there is no subject left for anything to be bad for. This is a fully worked-out materialism, not a modern development.
Hobbes revived it in the seventeenth century in an uncompromising form, holding that everything real is body in motion, thought included. He was arguing against Descartes' thinking substance, and the disagreement between them set the terms for the mind-body problem as it is still discussed.
Modern philosophers usually prefer physicalism, and the change of name is substantive. "Matter" suggests solid stuff, whereas physics describes fields, energy, forces and probability distributions, none of which are matter in the everyday sense. The claim is therefore that reality is exhausted by whatever a completed physics describes — which introduces a well-known difficulty. If physicalism means "everything is as current physics says," it is almost certainly false, since physics is incomplete. If it means "everything is as some future completed physics will say," it is hard to know what has been asserted. This is called Hempel's dilemma, and physicalists have proposed various ways around it without full agreement.
The case forWhy it's the default.
The evidence of dependence is overwhelming. Every mental capacity we know of can be altered by altering the brain — anaesthesia, injury, pharmacology, developmental disorders — with a specificity that would be baffling if minds were independent of matter. And the history of science has been a long series of phenomena once thought to require non-physical explanation being explained physically: life, heat, disease, inheritance. Materialism has an excellent track record.
The case againstWhat it hasn't explained.
Consciousness is the standing difficulty. A complete physical account of neural processing appears to leave open why any of it is accompanied by experience — the point pressed by Mary's Room and the zombie argument. Physicalists respond in several ways: that the gap is epistemic rather than metaphysical, that introspection misrepresents experience, or by adopting property dualism, which concedes the strict version.
Abstract objects. Numbers, sets and propositions do not appear to be located anywhere or made of anything, yet mathematics seems to be about something. Materialists must either find a physical account of them or argue they do not exist in the relevant sense, and both routes are contested.
Normativity. Moral facts, if there are any, are hard to place among physical facts. Some materialists identify them with natural properties; others conclude there are none, which is a substantial commitment rather than a free consequence.