The role of Shift Register Cascades in Cryptography?
Linear Feedback Shift Registers can not safely be used as Cryptographically Secure Pseudo-Random Number Generator (e.g. for the keystream of a stream cipher), because the state  of any LFSR is easily recovered from this output. Even it's structure can, using e.g. the Berlekamp-Massey algorithm.

In cryptography, Shift Register Cascades combine multiple LFSRs (or variants) into hopefully more secure CSPRNGs. Examples include the Alternating Step Generator, and A5/1. Arguably, the modern Trivium is a sort of Shift Register Cascade (which does not use clock control like the previous two, but instead uses a more complex feedback scheme).

Shift Register Cascades tend to inherit the main quality of LFSRs: simple hardware implementation.