The on-site measurement of radon-in-water concentrations relies on extraction of radon from the water followed by its detection by means of a mobile radon-in-air monitor. Many applications of radon as a naturally occurring aquatic tracer require the collection of continuous radon concentration time series, thus necessitating the continuous extraction of radon either from a permanent water stream supplied by a water pump or directly from a water body or a groundwater monitoring well. Essentially, three different types of extraction units are available for this purpose: (i) a flow-through spray chamber, (ii) a flow-through membrane extraction module, and (iii) a submersible (usually coiled) membrane tube. In this paper we discuss the advantages and disadvantages of these three methodical approaches with particular focus on their individual response to instantaneously changing radon-in-water concentrations. After a concise introduction into theoretical aspects of water/air phase transition kinetics of radon, experimental results for the three types of extraction units are presented. Quantitative suggestions for optimizing the detection setup by increasing the water/air interface and by reducing the air volume circulating through the degassing unit and radon detector are made. It was shown that the flow-through spray chamber and flow-through membrane perform nearly similarly, whereas the submersible membrane tubing has a significantly larger delay in response to concentration changes. The flow-through spray chamber is most suitable in turbid waters and to applications where high flow rates of the water pump stream can be achieved (e.g., where the power supply is not constrained by field conditions). The flow-through membrane is most suited to radon extraction from clear water and in field conditions where the power supply to a water pump is limited, e.g., from batteries. Finally, the submersible membrane tube is most suitable if radon is to be extracted in situ without any water pumping, e.g., in groundwater wells with a low yield, or in long-term time series, in which short-term variations in the radon concentration are of no relevance.