Embedded systems powered from time-varying energy harvesting sources traditionally operate using the principles of energy-neutral computing: over a certain period of time, the energy that they consume equals the energy that they harvest. This has the significant advantage of making the system ‘look like’ a battery-powered system, yet typically results in large, complex and expensive power conversion circuitry and introduces numerous challenges including fast and reliable cold-start. In recent years, the concept of transient computing has emerged to challenge this traditional approach, whereby low-power embedded systems are enabled to operate as usual while energy is available but, after loss of supply, can quickly regain state and continue where they left off. This paper provides a summary of these different approaches.