Luria was born in Kazan, a small town east of Moscow. He entered Kazan University when he was sixteen, and graduated with a degree at the age of nineteen. While a student, he established the Kazan Psychoanalytic Association.
In 1923, his work with reaction times related to thought processes earned him a position at the Institute of Psychology in Moscow. There, he developed the "combined motor method", which helped diagnose individuals' thought processes. Although he first published works about this research in 1932, these works were disallowed to be published by the Soviet Union, and were published in Russian for the first time in 2002.
In 1924, Luria met Lev Semionovich Vygotsky, who would influence him greatly. Along with Alexei Nikolaivitch Leontiev, these psychologists began developing a new type of psychology. This approach, coined as "cultural", "historical", and "instrumental" psychology dealt with the human psychological processes, with a heavy emphasis placed on language.
His work truly began in the 1930s, when Luria explored Central Asia, investigating various psychological changes (including perception, problem solving, and memory). He also studied identical and fraternal twins in large residential schools to determine various factors. In the late 1930s, he went to medical school, party to escape the Great Purges being carried out by Josef Stalin. He specialized in the study of aphasia, focusing on the relation between language and thought (as he had been doing). Eventually, he developed an effective treatment to aphasia.
The onset of World War II made Luria extremely valuable to the Soviets, because of his vast knowledge of thought processes. Meanwhile, Luria was able to study the large number of people with brain injuries, creating a symbiotic relationship.
Following the war, Luria continued his work as normal. For a period of time, he was removed from the Institute of Psychology, mainly as a result of a flare of anti-Semitism. He studied mentally retarded children for much of this time. In the late 1950s, Luria was allowed to return to work, where he remained, until his death from heart failure in 1977.
His two main case studies, both published a few years before his death, described a man with an exceptional yet idiosyncratic memory (1968), while the other described a man with a traumatic brain injury (1972). These case studies illustrate Luria's main methods of combining classical and remediational approaches; these methods form the basis of late 20th century cognitive science.