Salinity is a growing problem affecting soils and agriculture in many parts of the world. The presence of salt in plant cells disrupts many basic metabolic processes, contributing to severe negative effects on plant development and growth. This review focuses on the effects of salinity on chloroplasts, including the structures and function of these organelles. Chloroplasts house various important biochemical reactions, including photosynthesis, most of which are considered essential for plant survival. Salinity can affect these reactions in a number of ways, for example, by changing the chloroplast size, number, lamellar organization, lipid and starch accumulation, and interfering with cross-membrane transportation. Research has shown that maintenance of the normal chloroplast physiology is necessary for the survival of the entire plant. Many plant species have evolved different mechanisms to withstand the harmful effects of salt-induced toxicity on their chloroplasts and its machinery. The differences depend on the plant species and growth stage and can be quite different between salt-sensitive (glycophyte) and salt-tolerant (halophyte) plants. Salt stress tolerance is a complex trait, and many aspects of salt tolerance in plants are not entirely clear yet. In this review, we discuss the different mechanisms of salt stress tolerance in plants with a special focus on chloroplast structure and its functions, including the underlying differences between glycophytes and halophytes.