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