Orthogonal frequency division multiplexing (OFDM) is one of the representative integrated sensing and communication (ISAC) waveforms, where sensing and communications tend to be assigned with different resource elements (REs) due to their diverse design requirements. This motivates optimization of resource allocation/waveform design across time, frequency, power and delay-Doppler domains. Therefore, this article proposes two cross-domain waveform optimization strategies for OFDM-based ISAC systems, following communication-centric and sensing-centric criteria, respectively. For the communication-centric design, to maximize the achievable data rate, a fraction of REs are optimally allocated for communications according to prior knowledge of the communication channel. The remaining REs are then employed for sensing, where the sidelobe level and peak to average power ratio are suppressed by optimizing its power-frequency and phase-frequency characteristics. For the sensing-centric design, a `locally' perfect auto-correlation property is ensured by adjusting the unit cells of the ambiguity function within its region of interest (RoI). Afterwards, the irrelevant cells beyond RoI, which can readily determine the sensing power allocation, are optimized with the communication power allocation to enhance the achievable data rate. Numerical results demonstrate the superiority of the proposed communication-centric and sensing-centric waveform designs for ISAC applications.