The bilingual advantage in cognitive switching has been extensively documented in the literature (e.g., Bialystok, 2011; Bialystok, 2015). This thesis focuses on the cognitive gains of bilinguals in task-switching, specifically. If we assume that bilinguals outperform monolinguals in non-verbal task-switching (e.g., Prior & MacWhinney, 2010; Barac & Bialystok, 2012) due to frequent switching between languages in different contexts of their lives, we would also expect bilinguals to experience cognitive gains in verbal task-switching tests and in switching between possible interpretations of potentially ambiguous sentences. However, the cognitive switching literature has thus far failed to establish a link between verbal switching and non-verbal switching to support the explanation that non-verbal switching advantages in bilinguals may be attributed to the manipulation of verbal resources. This thesis investigates the connection between non-verbal and verbal task-switching, as well as ambiguity resolution in complex sentences, in order to determine the level of domain-generality or domain-specificity of cognitive switching. Additionally, the thesis aims to examine whether switching ability is responsible for language processing, with a focus on transient ambiguity. Leveraging the complex linguistic backgrounds in secondary schools in Hong Kong, this thesis also investigates the impact of diglossia, biliteracy, and medium of instruction on cognitive and/or sentence processing switching abilities. After exploring the educational, linguistic, and SES backgrounds of secondary school students in Hong Kong, Part 1 of the dissertation examines the relationship between non-verbal task-switching and verbal task-switching using cued task-switching paradigms in the auditory modality. Part 2 of the dissertation explores the links between cognitive task-switching and the interpretation of auditorily presented subject and object relative clauses in Chinese L1. Students from Hong Kong secondary schools with different mediums of instruction participated in the study. Both empirical studies in the two parts of the dissertation failed to find convincing evidence of a strong link between different types of switching, either between cognitive verbal and non-verbal switching or between cognitive switching and language processing. By delving into inter-school and inter-L1 differences, this thesis was able to identify the adverse impact of a Chinese diglossic environment on a student’s switching ability, due to a low level of frequent switching between languages (in our diglossic students, between oral Cantonese and written Mandarin) in the same context. These results present key educational considerations for diglossic education systems, where the high language in diglossia is used for retrieval while another low language is used for learning in the same schooling system. The findings of this thesis can inspire future research on the relationship between diglossia, medium-of-instruction policies, and cognitive-linguistic switching.