Why are they interesting?

There are many open problems and puzzles that are left unanswered by the standard model of particle physics.

Hence, many people search for a theory beyond standard quantum field theory and models beyond the standard model of particle physics.

We all agree that your theory is crazy, but is it crazy enough? Niels Bohr

The Standard Model is incapable of shedding light on the dynamics underlying electroweak symmetry breaking or explaining the structure of quarks, leptons, and their mass pattern at a fundamental level. The theory of inflation, in spite of its stunning conceptual successes, could not be linked univocally with a unified theory of particle physics. Moreover, the ubiquitous phenomenon of eternal inflation has changed the perspective on the outcome of an inflationary universe and its properties. We have plausible explanations for the cosmic baryon asymmetry, but we lack any conclusive empirical confirmation. The nature of dark matter is still unknown. The observed value of the cosmological constant is hard to reconcile with the rules of effective field theory, and quantum gravity is still beyond our grasp. None of these problems are new, and theoreticians have been tackling them for decades. What is changing is the feeling that the paradigm that so successfully led to the Standard Model may not be the right tool to make further progress. There is a widespread sensation that the organising principles based on symmetry and separation of scales, which follow from an effective quantum field theory approach, in spite of their triumphs, must be superseded by new organising principles. Physicists are in search for new conceptual paradigms, which is another symptom of a phase of crisis.The Dawn of the Post-Naturalness Era by Gian Francesco Giudice

Overview

Great general essays for possible approaches to search for new theories are:

• Reflections on the Evolution of Physical Theories by Henri Bacry
• Missed Opportunities by Freeman Dyson
• The Dawn of the Post-Naturalness Era by Gian Francesco Giudice

In his famous essay The Structure of Scientific Revolutions [10], the science historian Thomas Kuhn identifies a pattern in the development of scientific theories that is common to all revolutions in science. By freely reinterpreting (and simplifying) Kuhn’s structure, I can distinguish three phases in the process. The phase of discovery is when new conceptual breakthroughs and experimental results lead to the emergence of a new theory that departs from old paradigms. This is followed by a phase of consolidation, in which the theory is understood at a much deeper level and confirmed by precise measurements. This process has the effect of transforming the new theory into the established paradigm of normal science. Inescapably, this is superseded by a phase of crisis, in which the normal theory can no longer address new conceptual questions or explain experimental data. This phase is characterised by the search for new paradigms and marked by periods of confusion and frustration. Finally a paradigm shift occurs, which results in a radical departure from normal science, thus activating a new phase of discovery and marking the beginning of a new cycle. The Dawn of the Post-Naturalness Era by Gian Francesco Giudice