This paper reviews the smallness, modularity and reactor-design aspects of emerging small modular reactors (SMRs). It is shown that small (whether in physical size or power level) reactors are not new, but offer economic and flexibility advantages that allow their use in a variety of applications. The different definitions of modularity are reviewed, including modularity in design, process intensification, manufacturing and construction. It is shown that these forms of modularity when applied to SMRs have some advantages, but also have some challenges that need to be addressed if their full potential is to be realized. Even if these forms of modularity are not fully utilized, the lower power (≤300 MW electrical) of SMRs allows the formation of larger power plants by incremental addition of reactor units, in the so-called scale modularity. The paper reviews the unique features of emerging SMR designs, and compares them to those of the early era of nuclear power. It is shown that while many modern SMR designs incorporate well-proven features that were tested and proven in early reactors. others introduce aspects of Generation IV reactors, in terms of inherent and/or passive safety. Given the promise of SMRs as means to reduce greenhouse gas emissions and their ability to supply reliable and base-load power, the licensing of such reactors by national regulators will provide a boost to their acceptability and adaptability as a player in combating climate change.