Algorithmic intuition for logarithmic complexity

I believe I have a reasonable grasp of complexities like $\mathcal{O}(1)$, $\Theta(n)$ and $\Theta(n^2)$. In terms of a list, $\mathcal{O}(1)$ is a constant lookup, so it's just getting the head of the list. $\Theta(n)$ is where I'd walk the entire list once, and $\Theta(n^2)$ is walking the list once for each element in the list. Is there a similarly intuitive way to grasp $\Theta(\log n)$ other than just knowing it lies somewhere between $\mathcal{O}(1)$ and $\Theta(n)$?