Waveform design has served as a cornerstone for each generation of mobile communication systems. The future sixth-generation (6G) mobile communication networks are expected to employ larger-scale antenna arrays and exploit higher-frequency bands for further boosting data transmission rate and providing ubiquitous wireless sensing. This brings new opportunities and challenges for 6G waveform design. In this article, by leveraging the super spatial resolution of large antenna arrays and the multi-path spatial sparsity of highfrequency wireless channels, we introduce a new approach for waveform design based on the recently proposed delay-Doppler alignment modulation (DDAM). In particular, DDAM makes a paradigm shift of waveform design from the conventional manner of tolerating channel delay and Doppler spreads to actively manipulating them. First, we review the fundamental constraints and performance limitations of orthogonal frequency division multiplexing (OFDM) and introduce new opportunities for 6G waveform design. Next, the motivations and basic principles of DDAM are presented, followed by its various extensions to different wireless system setups. Finally, the main design considerations for DDAM are discussed and the new opportunities for future research are highlighted.