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Newer approaches
One limitation with Einstein's work was at first his rejection, and then his ignorance of quantum theory (which he acknowledged as the years went on.) But even today, scientists who are familiar with quantum theory are also having difficulty coming up with a unified theory.
There are many approaches being considered, but the most promising, according to APS, involves string theory. The theory "describes all elementary particles as vibrating strings, with different modes of vibration producing different particles."
In the 1980s, physicists (led by John Schwarz and Michael Green) concluded that string theory could work because of its vibrations. Similar to how a violin plays different notes, the theory went, different vibrations in strings of nature would create different particles. In the mid-1990s, Edward Witten proposed more exact theories of string theory, now called M-theory. His work expanded string theory dimensions from six to seven, and showing new ingredients of the theory (including branes, or membrane-like objects in various dimensions.)
Work in this field is very much emerging, but researchers are trying to learn more physical properties of the string by studying the subatomic particles produced in particle accelerators, such as the Large Hadron Collider. Among other directions, the LHC experiments are intended to look for supersymmetry, or a supposed mathematical property where every particle species would have a partner particle species.
Physicists caution that a weakness of string theory is it has not yet been confirmed by data. There are also other approaches to unified field theory, such as quantum gravity, which tries to describe gravity in the terms of quantum mathematics.