Hearing impairment interferes with speech communication. Hearing aids are designed to provide amplification for individuals with poor auditory sensitivity. Signal processing algorithms are implemented in hearing aids to further improve speech understanding and to reduce listening effort in noise. When listening effort is reduced, fewer resources are assumed to be needed for speech perception and more resources would thus be freed for cognitive processing of speech. However, this effect has only been reported in young adults with normal hearing, not in hearing aid users. Cognitive abilities, which vary between individuals, have been shown to influence the ability to benefit from hearing aids. Specifically, it is not yet known how individual differences in cognitive abilities interact with signal processing to reduce listening effort. Also, the relationship between cognition and aided speech recognition performance, as a function of acclimatization processes in new hearing aid users, has not been studied previously.This thesis investigated the importance of cognition for speech understanding in experienced and new hearing aid users. Four studies were carried out. In the first three studies (reported in Papers 1 to 3), experienced hearing aid users were tested and the aims were 1) to develop a cognitive test, called the Sentence-final Word Identification and Recall (SWIR) test, to measure the effects of a noise reduction algorithm on processing of highly intelligible speech (everyday sentences). SWIR performance is argued to reflect the amount of remaining resources upon successful speech perception; 2) to investigate, using the SWIR test, whether hearing aid signal processing would affect memory for heard speech; 3) to test whether the effects of signal processing on the ability to recall speech would interact with background noise and individual differences in working memory capacity; and 4) to explore the potential clinical application of the SWIR test by examining the relationship between SWIR performance and self-reported hearing aid outcome. In the fourth study (reported in Paper 4), the aim was 5) to examine the relationship between cognition and speech recognition in noise in new users using various models of hearing aids over the first six months of hearing aid use.Results of the studies reported in Papers 1 and 3 demonstrated that, for experienced users, noise impairs the ability to recall intelligible speech heard in noise. Noise reduction freed up cognitive resources and alleviated the negative impact of noise on memory when speech stimuli were presented in background noise consisting of speech babble spoken in the listener's native language but not in a foreign language. The possible underlying mechanisms are that noise reduction facilitates auditory stream segregation between target and irrelevant speech and reduces the attention captured by the linguistic information in irrelevant speech. In both studies, the effects of noise reduction and SWIR performance were modulated by individual differe...