There are a number of functions paragraphs play in discourse studies. For example, it encourages a writer to give adequate focus to the various aspects of his or her message; and it facilitates the identification of one idea in an essay to another idea. Some classical second language writers (for example: Stern, 1976; Halliday & Hasan, 1976; Warriner, 1988; Lunsford & Connors, 1995; Driscoll & Brizee, 2000; Langan, 2001; Sekyi-Baidoo, 2003; Kirzner& Mandell, 2007; and Beare, 2012) on discourse studies have focused on key theoretical issues of paragraph theory such as: definition, types, structure and elements. Modern writers such as Bailey (2011), Rolls & Wignell (2013), Nordquist (2019) have also contributed to studies on paragraph theory. Some university students find it perplexing observing all the elements and constituents of the paragraph theory. The purpose of the paper was, therefore, to find out factors accounting for students' problems in construction of paragraphs. This chronological paper traced the various theories of paragraph from 1970s to the 2000s, and analysed thirty (30) essay-based texts of university students in a descriptive way. Again, two texts (one each) from a non-native academic of English and a native academic of English were analysed. The results from the texts of student participants showed students' paragraph writing flaws in areas of concluding sentence, and coherence. The study, therefore, recommended that second language teachers should pay extra attention to students' paragraphs, especially in writing of concluding sentences, and observance of paragraph coherence.