Many of us teachers have heard students complain about how fast native speakers of English speak or how words sound different in isolation from when they are spoken in context. Divergent justifications notwithstanding, the most determining factor might be claimed to be connected speech referring to “the changes which conventional word forms undergo due to the temporal and articulatory constraints upon spontaneous, casual speech” (Hieke, 1987, p. 41). Also called connected speech processes (CSPs), these changes occur when words are pronounced in spoken discourse (i.e. spontaneous or conversational speech) and originate from linguistic context, speech rate, and register. Connected speech is essential to speech recognition and text-to-speech technologies as well as English language learners (ELLs). Without it, speech may sound disconnected and artificial and result in serious intelligibility problems in oral communication. In this regard, it might be viewed as the most salient pronunciation feature in listening comprehension. For that reason, ELLs should be furnished with the relevant knowledge and competence, that is, the ability to articulate words in isolation and context. This paper consequently aims to tackle the CSPs in English by (i) characterizing the main classifications, (ii) discussing previous research findings, and (iii) presenting practicable methods for teaching them to ELLs. It thereby intends to contribute to an augmentation in learner and teacher awareness about the CSPs.