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Let $p$ be an odd prime and let $E$ be an elliptic curve defined over anumber field $F$ with good reduction at primes above $p$. In this surveyarticle, we give an overview of some of the important results proven for thefine Selmer group and the signed Selmer groups over cyclotomic towers as wellas the signed Selmer groups over $\mathbb{Z}_p^2$-extensions of an imaginaryquadratic field where $p$ splits completely. We only discuss the algebraicaspects of these objects through Iwasawa theory. We also attempt to give someof the recent results implying the vanishing of the $\mu$-invariant under thehypothesis of Conjecture A. Moreover, we draw an analogy between the classicalSelmer group in the ordinary reduction case and that of the signed Selmergroups of Kobayashi in the supersingular reduction case. We highlightproperties of signed Selmer groups (when $E$ has good supersingular reduction)which are completely analogous to the classical Selmer group (when $E$ has goodordinary reduction). In this survey paper, we do not present any proofs,however we have tried to give references of the discussed results for theinterested reader.

Conjecture A and $\mu$-invariant for Selmer groups of supersingular elliptic curves