A conjecture of S. Yau asserts that if two isolated surface singularities in C³ have the same monodromy zeta-function and the same abstract topology, then they must also share the same embedded topology. This conjecture was disproved by E. Artal Bartolo, who explicitly constructed a pair made of two superisolated surface singularities with identical zeta-functions and abstract topologies but distinct embedded topologies. Today, any pair exhibiting this phenomenon is referred to as a Zariski pair of surface singularities. Subsequent research has further explored Zariski pair-like phenomena, resulting in several recent developments in the field. In this talk, I will present a concise introduction to this subject and its main results.