The newest developments in the investigation of redshift quantization and variability are summarized and several approaches to cosmological models consistent with aspects of the data are discussed. The periodicities present when redshifts are referred to the Cosmic Background Radiation rest frame appear to be very precisely described by a series of period-doubling sequences based upon the ninth-root of 2 times the speed of light. Several examples of redshift quantization and variability are discussed to illustrate the periods, the CBR association and the dependence upon galaxy properties. Possible cosmological models involving properties of time, including a form of three-dimensional time and possible time networks, are introduced. Such models appear to have the potential to admit quantized and variable redshifts while remaining consistent with local continuous physical theory.