This paper discusses various problems related to the teaching of English grammar at Korean universities. We first discuss whether English grammar should be taught at universities, and, if it is, what kind of English grammar needs to be taught. We propose that the English grammar we teach to Korean undergraduate students be eclectic in the sense that the traditional grammar established by Jespersen and others be the major source of instruction, supplemented, if necessary, by school grammar and also by linguistically oriented grammars such as generative grammar or cognitive grammar. Then we discuss the content of the English grammar that should be included in the curriculum : (i) present perfect vs. past, (ii) will vs. be going to, (iii) must vs. have to, (iv) may vs. can, (v) infinitives vs. gerunds, (vi) conative constructions, and (vii) the passive.