An m-sequence of degree n is a binary sequence of 0's and 1's of period $2^d-1$ generated by an n-stage linear feedback shift register. These sequences have several pseudo-randomness properties that make them useful in many communications applications (cryptography, radar, CDMA wireless, etc). There is a bijection between m-sequences and primitive polynomials over GF(2). Numerous solved and unsolved problems about m-sequences and their randomness will be discussed.