Limitations of boolean and arithmetic circuits Much of modern cryptography is based around working with boolean or arithmetic circuits. For example in Multi-Party Computation the 'famous' results allow for the secure computation of any function that can be represented as a boolean or arithmetic circuit.

I am wondering what the limits of these circuits are, what are some examples of functions are we not able to compute securely --- that is what functions are not representable as a boolean or arithmetic circuit? And in the real world does this reduce the effectiveness of modern cryptography or are these circuits enough to implement everything we require?
The question should be which functions can we build a small circuit to solve. Any function mapping a fixed number of bits to a fixed output can be represented as a boolean circuit. But it may be very large. 
This brings is to a difficult topic with few lower bounds: https://en.m.wikipedia.org/wiki/Circuit_complexity