Olaf vs Cho'Gath

Don't run too early at low health: Berserker Rage (passive) gives you attack speed and life steal based on your missing health.

Throw Undertow (Q) close to you or just behind your target, then pick up the axe: its cooldown is reduced, or fully refunded if you pick it up late enough.

Weave Reckless Swing (E) between your autos: its true damage ignores resistances, and each auto lowers its cooldown by 1 second.

Cast Ragnarok (R) as you charge their carry: you're freed from all CC, nothing stops you anymore, and each hit on a champion extends the effect.

Keep moving against him: Rupture (Q) strikes an area on the ground, and an enemy standing still takes a knock-up, damage and a slow.

Punish him when he goes for last hits: Carnivore (passive) restores health and mana for each unit he kills, and he lasts a long time in lane if you let him farm.

If you have range, keep your distance: his kit has no dash, only the slows from Rupture (Q) and Vorpal Spikes (E).

Don't stay in melee range at low health when Feast (R) is up: its true damage ignores your resistances, even if you're a tank.