This thesis investigated speech recognition by native (L1) and non-native (L2) listeners (i.e., native English and Korean speakers) in diverse adverse conditions using electroencephalography (EEG) and behavioural measures. Study 1 investigated speech recognition in noise for read and casually produced, spontaneous speech using behavioural measures. The results showed that the detrimental effect of casual speech was greater for L2 than L1 listeners, demonstrating real-life L2 speech recognition problems caused by casual speech. Intelligibility was also shown to decrease when the accents of the talker and listener did not match when listening to casual speech as well as read speech. Study 2 set out to develop EEG methods to measure L2 speech processing difficulties for natural, continuous speech. This study thus examined neural entrainment to the amplitude envelope of speech (i.e., slow amplitude fluctuations in speech) while subjects listened to their L1, L2 and a language that they did not understand. The results demonstrate that neural entrainment to the speech envelope is not modulated by whether or not listeners understand the language, opposite to previously reported positive relationships between speech entrainment and intelligibility. Study 3 investigated speech processing in a two-talker situation using measures of neural entrainment and N400, combined with a behavioural speech recognition task. L2 listeners had greater entrainment for target talkers than did L1 listeners, likely because their difficulty with L2 speech comprehension caused them to focus greater attention on the speech signal. L2 listeners also had a greater degree of lexical processing (i.e., larger N400) for highly predictable words than did native listeners, while native listeners had greater lexical processing when listening to foreign-accented speech. The results suggest that the increased listening effort experienced by L2 listeners during speech recognition modulates their auditory and lexical processing.