Phonological research has demonstrated that English intonation, variably referred to as prosody, is a multidimensional and multilayered system situated at the interface of information structure, morphosyntactic structure, phonological phenomena, and pragmatic functions. The structural and functional complexity of the intonational system, however, is largely under-addressed in L2 pronunciation teaching, leading to a lack of spontaneous use of intonation despite successful imitation in classrooms. Focusing on contrastive and implicational sentence stress, this study explored the complexity of the English intonation system by investigating how L1 English and Mandarin-English L2 speakers use multiple acoustic features (i.e., pitch range, pitch level, duration, and intensity) in signaling contrastive and implicational information and how one acoustic feature (maximum pitch level) is affected by information structure (contrast), morphosyntactic structure (phrasal boundary), and a phonological phenomenon (declination) in L1 English and Mandarin-English L2 speakers' speech. Using eye-tracking technology, we also investigated (1) L1 English and Mandarin-English L2 speakers' real-time processing of lexical items that carry information structure (i.e., contrast) and typically receive stress in L1 speakers' speech; (2) the influence of visual enhancement (italics and bold) on L1 English and Mandarin-English L2 speakers' processing of contrastive information; and (3) L1 English and Mandarin-English L2 speakers' processing of pictures with contrastive information. Statistical analysis using linear mixed-effects models showed that L1 English speakers and Mandarin-English L2 speakers differed in their use of acoustic cues in signaling contrastive and implicational information. They also differed in the use of maximum pitch level in signaling sentence stress influenced by contrast, phrasal boundary, and declination. We did not find differences in L1 English and Mandarin-English L2 speakers' processing of contrastive and implicational information at the sentence level, but the two groups of participants differ in their processing of contrastive information in passages and pictures. These results suggest that processing limitations may be the reason why L2 speakers did not use English intonation spontaneously. The findings of this study also suggest that Complexity Theory (CT), which emphasizes the complex and dynamic nature of intonation, is a theoretical framework that has the potential of bridging the gap between L2 phonology and L2 pronunciation teaching.