He carried out his doctoral studies at Yale University in New Haven, Connecticut, United States, obtaining his Ph.D. in 1961 under the tutorship of Prof. F.M. Richards. He did post doctoral work with Prof. Fritz Lipmann at Rockefeller University and with Marshall Warren Nirenberg at NIH.
During the 1960s, his research was focused on protein synthesis, a field in which he made crucial contributions. In the 1970s he was a pioneer in studying the mechanism of hormonal induction of oocyte maturation.  His later research is focused in  two ubiquitous protein kinases, CK1 and CK2, involved in the phosphorylation of key cellular proteins.
He devoted much of his life to organizing activities for the scientific integration in Latin America especially through organizing series of training courses in molecular biology techniques,  and through the creation of the Latin American Network of Biological Sciences.
In recent years, Doctor Allende has been an promoter of science education through his personal commitment in several projects, like the Science Education Inquiry Based program, funded by the University of Chile, and through his participation in the Allende-Connelly Foundation, founded by him and his wife.
Though he retired from active science in 2009, he remains a professor at the Faculty of Medicine. He was also Research Vice President of the University of Chile.
He published his autobiography in 2010.