Chirped multilayer mirrors have permitted mode-locked lasers to routinely generate pulses in the sub-10 fs regime. Continuous progress in the design, manufacturing, and characterization of multilayer structures has led to ever more precise group-delay dispersion control over ever broader spectral ranges. The resultant few-cycle laser fields have opened the door to the generation and measurement of isolated attosecond pulses and led to the birth of attosecond metrology. Precision multilayer dispersion control over increasing bandwidth has gradually pushed the frontier of femtosecond technology to what has been thought to be its ultimate limit: the wave cycle of visible light, allowing routine generation of sub-100 attosecond pulses. Next-generation attosecond technology will be based on synthesized multi-octave waveforms; they are expected to advance the field in several ways: first, by permitting control of electronic motions with a force variable on the atomic time scale; second, by providing sub-femtosecond optical transients for attosecond nonlinear pump-probe spectroscopy; third, by producing attosecond pulses at Angstrom wavelengths, opening the door to four-dimensional imaging with atomic resolution in space and time. In this article, we address the enabling technology: chirped multilayers for spectral separation and recombination as well as precise dispersion control of multi-octave optical radiation spanning from the ultraviolet to the mid-infrared range. This cutting-edge optical technology provides the force engineerable on atomic-to-molecular time scales and brings about the next revolution in ultrafast science.