Circuitry (both digital and analog, including entire computers) can be built using hydraulics. Complex parts like logic gates, oscillators are present, but also "passive" things like accumulators, resistors, and valves -- it's all there.
They work in about the same way as electronic circuits do.
(But it's almost always less expensive to push electricity around than it is to push liquid around, and the parts are a lot smaller, so obviously electronic circuits are the usual winner.
Nonetheless, hydraulic circuits are still pretty common: See, for example, the valve body of an automatic transmission such as (mostly?) electronics-free 700R4.)
Coming from an EE background and doing some simple hydraulics work, it blew my mind that the various components are mainly just the right shapes of metal. In retrospect I don't know what else I could have been expecting, except that electronic components are generally made of some special substance. Talk about actual "bare metal" development.
There are limits to the propagation velocity of signals in both systems that are sometimes necessary to account for. Hydraulics tend to be slower, but it's still the same problem -- each just has different values to plug in and deal with.
Concerns about things like impedance matching and reflections are also the same.
They work in about the same way as electronic circuits do.
(But it's almost always less expensive to push electricity around than it is to push liquid around, and the parts are a lot smaller, so obviously electronic circuits are the usual winner.
Nonetheless, hydraulic circuits are still pretty common: See, for example, the valve body of an automatic transmission such as (mostly?) electronics-free 700R4.)