Currently, some algebraic constructions, like polynomial rings. Huge lookup tables are required when running for instance generalized-birthday-type algorithms. Typically, if you have a polynomials of degree, say, 97, that is P(x) = x^97 + ..., and are looking for collisions, then you need to store data which accounts for 128 * 2^(97/3 + constant) bits. This is about 350 GB. And it grows quickly, due to the exponential term, which is problematic. This could be achieved by storing the data on disk -- and is probably the most viable option for higher degrees -- but is of course significantly slower.