Béla Rerrich began fencing in 1937 with BEAC and later represented Toldi Miklós SE, Hitelbank, Budapesti Lokomotív, and Budapesti Törekvés. Though skilled in foil, his greatest results were in épée, with him winning four Hungarian individual championships and nine team titles. Rerrich competed in three Olympics as a member of the épée team: fifth in 1948 (London), fifth in 1952 (Helsinki), and silver in 1956 (Melbourne), winning Hungary’s first Olympic medal in the team épée. He was able to compete in the individual event in two of them (1952, 1956). He also won team bronze at the 1955 World Championships in Roma.
Rerrich earned a doctorate in political science and law in 1940 from Pázmány Péter University. He worked in physical education and teaching, and later for Hungarian Railway. After the 1956 Olympics, Rerrich did not return to Hungary, touring the US with Sports Illustrated before settling in Sweden. There he became head coach of the national fencing and pentathlon teams. Under his leadership Sweden won team épée gold at the 1976 Montréal Olympics. He also coached Björn Ferm, the 1968 Olympic champion in modern pentathlon. Rerrich ultimately took part in seven Olympics with the Swedish team.