Ultrasonics have been widely used for testing concrete in the hardened and fresh state. Serious advances have been made in the field throughout the last three decades in terms of wave analyses, hydration modeling while materials with various additives have been tested. However, from the ultrasonics point of view, most of the information is provided mainly by the traditional parameter of "pulse velocity" based on the initial waveform threshold crossing and secondary by the amplitude of the pulse. These features are very powerful, but their characterization capacity diminishes with the increasing heterogeneity of the material. Detailed measurements of phase velocity and attenuation as a function of frequency provide extended information since instead of a single pulse velocity value, they provide a whole curve of wave velocity or attenuation over the frequency range of interest. This allows to observe resonant peaks owing to the microstructure giving better possibilities for characterization and allowing the monitoring of the changes of the curve as the material evolves from viscous to solid. In this paper a summary of wave dispersion and attenuation measurements in cement paste and mortar is presented, supported by theoretical formulations considering the microstructure while challenges and potential improvements are discussed.