(1) Introduction: With older adults, cognitive intervention programs are most often used for preventing or reversing a decline in cognitive functions, but it has been recently noted that there are insufficient high-quality research studies that report the effects of cognitive intervention on the cognitive functioning of older adults. (2) Objective: To analyze the available evidence concerning the effect of cognitive interventions for improving or maintaining the general cognitive status of older adults who present different cognitive levels. (3) Method: a review of studies published between 2010 and 2019 using the following databases: PubMed, PsycINFO, Cochrane, Google Scholar, ProQuest and Medline. (4) Results: We selected 13 systematic reviews and/or meta-analyses. The results showed that the cognitive intervention programs improved general cognitive functioning and specific cognitive functions regardless of the initial cognitive level; that cognitive decline was slowed in older persons with dementia; and there was improvement in activities of daily living. Regarding duration of the results, benefits were maintained for periods of 2 months to 5 years. (5) Conclusion: Cognitive interventions have proven effective for maintaining and/or improving cognitive functioning in older adults regardless of their initial cognitive status. Even so, there are few studies that follow up these results to see whether they are maintained in the long term and whether there is transfer to other skills of daily life. However, we were able to observe in the present review how the participants’ cognitive level varied according to sociodemographic differences, and to identify which components of cognitive programs make them more effective. Based on the results found, we highlight the importance of designing cognitive intervention programs that meet these effectiveness criteria, in order to maximize the positive effects of such programs when working with a population of older adults.