Parabolic trough solar collector (PTC) is one of the solar thermal energy applications, which focuses sunlight to heat the heat transfer fluid (HTF) circulating through the receiver. Researchers have put forward several heat transfer models for PTCs, basing on laws of conservation. This paper summarized the one-dimensional (1-D) mathematical models under different assumptions and details for PTCs. All the heat transfer processes were considered: convection within the absorber, in the annulus and between the glass and ambient; conduction through glass cover, absorber and support brackets; radiation in the annulus and from the glass to the sky. Moreover, a simple algorithm was adopted to make the control equations linear and solve easily. The difference in accuracy for diverse 1-D models were presented and analyzed on the basis of the experimental data from Sandia National Laboratories. The 1-D models with various details were different in accuracy and complexity. It can choose an appropriate 1-D model under a certain condition, which can be used in investigating the thermal performance of a PTC. In addition, the most accurate 1-D model presented in this paper were precise enough compared with the three-dimensional (3-D) model from other paper. The average difference of outlet temperature between the most accurate simulation in this paper and test data was 0.65 degrees C, however it was 2.69 degrees C between the 3-D model and experiment results. The reason may be that there were more assumptions for 3-D models than 1-D models, therefore the error was bigger. (C) 2015 Elsevier Ltd. All rights reserved.