Renormalization group methods have been used for almost 50 years to obtain results for critical exponents of conformal field theories (CFTs), while relying on assumptions and approximations that are not rigorously justified. The agreement with experiments is good in many cases, e.g. the 3D Ising model, but disagreements between theory and experiment that have remained unresolved for decades also exist. This indicates that our understanding of critical phenomena may be incomplete. More recently, the numerical conformal bootstrap, a fully nonperturbative method, has proven to be very powerful in calculating critical exponents and other physical observables of CFTs. In this talk we will review the numerical conformal bootstrap method and discuss potential resolutions it has suggested for unsettled questions pertaining to critical phenomena in frustrated magnets and structural phase transitions. [please email alejandro.cabo_bizet@kcl.ac.uk for the zoom link]