Various scaling relations have long been established in the field of heterogeneous catalysis

but the resultant volcano curves inherently limit the catalytic performance of catalyst candidates. On the other hand

it is still very challenging to develop universal descriptors that can be used in various types of catalysts and reaction systems. For these reasons

several strategies have recently been proposed to break and rebuild scaling relations to go beyond the top of volcanoes. In this review

some previously proposed descriptors have been briefly introduced. Then

the strategies for breaking known and establishing new and more generalized scaling relations in complex catalytic systems have been summarized. Finally

the application of machine-learning techniques in identifying universal descriptors for future computational design and high-throughput screening of heterogeneous catalysts has been discussed.