We will consider field theory describing particle physics. More specifically we will concentrate on the electron self energy. That quantity comes out to be infinite and prevented the further application of that theory.
The first to consider this electron self energy were Lorentz and Abraham around 1900. After the introduction of quantum mechanics (1925) and the subsequent introduction of quantum field theory by Heisenberg and Pauli in 1929, no progress was made for quite some time. Weisskopf noted that within the quantum theory the electron self energy was still infinite, but only logarithmically. In 1948 the discovery of certain experimental facts led to further theoretical progress, including Kramer's idea of renormalizability and Feynman's introduction of the Feynman rules, a graphical presentation of the theory that simplified the calculations enormously. However, the theory was still not capable of treating theories with a symmetry. It took till 1971 to further advance the theory so far that weak interactions (a theory with a symmetry) could be described, with great success.