Abstract: ‍ ‍With the deepening construction of global information society， the shortage of spectrum resources is becoming increasingly prominent. Spectrum competition among various countries， functionalities， and military & civilian applications has basically taken shape. Specifically， spectrum competition between radar and wireless communication is the most intense. Therefore， joint radar and communication waveforms for spectrum sharing has attracted special attentions. In this paper， the research history of the joint waveform， along with its trend towards multi-dimensional modulation， are thoughtfully reviewed and discussed. Then， limitations of traditional joint waveforms and essential advantages of multi-dimensional joint waveforms are analyzed theoretically. Moreover， new degrees of freedoms beyond conventional time and frequency domains are developed and mined. According to which， several physically feasible multi-dimensional joint waveforms are designed. Finally， performances of the multi-dimensional joint waveforms are validated by simulations and outfield experiments. This paper attempts to point out the research direction for future joint radar sensing and wireless communication waveforms. Even more important， this paper aims to provide theoretical and technical solutions for China to deal with spectrum utilization contradictions including the high shortage of spectrum resources， the extremely fierce spectrum competition， the rapid growth of spectrum demands， and the low efficiency of current spectrum utilization.