Optoacoustic (photoacoustic) sensing employs illumination of transient energy and is typically implemented in the time domain using nanosecond photon pulses. However, the generation of high-energy short photon pulses requires complex laser technology that imposes a low pulse repetition frequency (PRF) and limits the number of wavelengths that are concurrently available for spectral imaging. To avoid the limitations of working in the time domain, we have developed frequency-domain optoacoustic microscopy (FDOM), in which light intensity is modulated at multiple discrete frequencies. We integrated FDOM into a hybrid system with multiphoton microscopy, and we examine the relationship between image formation and modulation frequency, showcase high-fidelity images with increasing numbers of modulation frequencies from phantoms and in vivo, and identify a redundancy in optoacoustic measurements performed at multiple frequencies. We demonstrate that due to high repetition rates, FDOM achieves signal-to-noise ratios similar to those obtained by time-domain methods, using commonly available laser diodes. Moreover, we experimentally confirm various advantages of the frequency-domain implementation at discrete modulation frequencies, including concurrent illumination at two wavelengths that are carried out at different modulation frequencies as well as flow measurements in microfluidic chips and in vivo based on the optoacoustic Doppler effect. Furthermore, we discuss how FDOM redefines possibilities for optoacoustic imaging by capitalizing on the advantages of working in the frequency domain.