In a one-bit quantization scheme, bandlimited functions are represented for each sampling density by sequences that take only two values and this is done in such a way that approximations of the original functions can be obtained by convolving these sequences with appropriately chosen filters. A popular example is sigma-delta quantization, which produces the representative bitstreams of an input function via a symbolic dynamics associated with a nonlinear discrete dynamical system forced by the function. We present a new framework and improved techniques for the error analysis of sigma-delta quantization as well as various refined error estimates and open questions in the field.