Aims and objectives/purpose/research questions: The degree of overlap across languages in bilingual semantic memory has been debated in the cognitive bilingual literature for decades. This paper focuses on theory and recent evidence addressing the questions of whether translation-equivalent words in a bilingual person’s two languages access common core-meaning representations and whether long-standing semantic/conceptual associations among words are language-general or language-specific. Design/methodology/approach: We explain a theoretical approach to this problem and review recent evidence that addresses it. The empirical work cited used primarily memory tasks in which the languages of the word stimuli or responses changed from encoding to test. Data and analysis: Several studies are reviewed. In most cases, data were analyzed using an analysis of variance. Findings/conclusions: Robust between-language priming was observed for concrete nouns, abstract nouns, verbs, and adjectives using a variety of specific tasks, indicating that the semantic representations of translation equivalents overlap. The reduction in priming relative to within-language conditions could be explained in some cases by repetition of language-specific processes in the within-language conditions. Results of repetition-priming and false-memory experiments that involved semantic associations showed that category–exemplar, noun–verb, antonym, and other semantic relationships are shared across languages in a common semantic system. Originality: Many of the results are interpreted with respect to questions that have not been addressed in previous work. Significance/implications: The nature of semantic system integration is important for understanding bilingual cognition. Episodic memory tasks can be a useful way to study the organization of core-meaning representations in bilinguals, and indicate that these representations are shared across languages. However, these procedures do not capture other aspects of semantic representation that may differ across languages.