<p>Manipulating the phase of an optical wave over time and frequency gives full control to the user to implement a wide variety of energy preserving transformations directly in the analogue optical domain. These can be achieved using widely available linear mechanisms, such as temporal phase modulation and spectral phase filtering. The techniques based on these linear optical wave energy redistribution (OWER) methods are inherently energy efficient and have significant speed and bandwidth advantages over digital signal processing. We describe several recent OWER methods for optical signal processing, including denoising passive amplification, real-time spectrogram analysis, passive logic computing, and more. These functionalities are relevant whenever the signal is found on a classical or quantum optical wave, or could be upconverted from radio frequencies or microwaves, and they are of interest for a wide range of applications in telecommunications, sensing, metrology, biomedical imaging, and astronomy. The energy preservation of these methods makes them particularly interesting for quantum optics applications. Furthermore, many of the individual components have been demonstrated on-chip, enabling miniaturization for applications where size and weight are a main constraint.</p>