Digital Low-dropout (DLDO) regulators have been widely utilised for highly-efficient fine-grained power delivery and management in system-on-chips (SoCs) due to their process scalability, ease of integration, and low-voltage operation. However, conventional DLDOs suffer gravely from the power-speed tradeoff, which arises from the use of sampling clocks. To obtain reasonable performance in the undershoot and recovery during load transient states, a large output capacitor is inevitably required in these DLDOs. Moreover, they inherently involve large steady-state voltage ripples and poor power-supply rejection (PSR). These limitations of synchronous DLDOs and their counter measures are thoroughly discussed in this paper. Various design strategies of major building blocks, i.e. comparators and power transistor arrays, are explained in detail with examples. Architectural advances are also expounded including state-of-the-art DLDO architectures such as clock-boosted synchronous, analog-assisted synchronous, asynchornous, event-driven, and hybrid DLDOs. These state-of-the-art DLDOs do not only address the power-speed tradeoff and achieve fast load transient responses, but also can eliminate the use of an output capacitor in some cases. Moreover, some hybrid DLDOs successfully removed the steady state ripples and achieve high PSR. All of these DLDO are compared on basis of their performance metrics and figure-of-merits (FOMs).