A radio map is a collection of signal fingerprints labeled with their collected locations. It is known that the performance of a fingerprint-based positioning systems is closely related to the precision and accuracy of the underlying radio maps. However, little has been studied on the performance of radio maps in relation to the fingerprint collection methods and the radio map models, which determine the accuracy and precision of radio maps, respectively. This paper evaluates the performance of various radio map construction methods in both indoor and outdoor environments. Four radio map construction methods, i.e., a point-by-point manual calibration, a walking survey, a semisupervised learning-based method, and an unsupervised learning-based method, have been compared. We also evaluate the performance of various types of radio map models that represent the characteristics of collected fingerprints. To demonstrate the importance of the radio map model, a new model named signal fluctuation matrix (SFM) was developed, and its performance was compared with that of the three conventional radio map models, respectively. The evaluation revealed that the performance of the radio maps was very sensitive to the design of radio map models and the number of fingerprints collected at each location. The performance achieved by SFM-based positioning was comparable with that of the other models despite using a small number of fingerprints.