Why oak? Oak is slightly porous: it allows micro-oxygenation that softens tannins and develops complexity. It also imparts flavour compounds.
New vs old oak: New barrels impart maximum flavour (vanilla, spice, toast). Second- or third-use barrels add oxygen exposure with minimal flavour. Large old casks (foudres, botti) used in Barolo add almost no oak flavour: they're about slow oxidation only.
French vs American oak: French oak = fine-grained, subtle, elegant (cedar, spice, smoke). American oak = wider-grained, bolder (vanilla, coconut, dill). Common in Rioja and California.
Toast level: Light toast preserves wood tannin. Medium toast adds vanilla and spice. Heavy toast (char) adds mocha, espresso, dark chocolate.
Alternatives: Stainless steel preserves freshness. Concrete (tanks or eggs) adds texture without flavour. Amphora/clay pots are ancient vessels now used by natural winemakers: micro-porous, flavour-neutral.