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Cylindrical contact homology is arguably one of the more notorious Floer-theoretic constructions. Jointly with Hutchings we have managed to redeem this theory in dimension 3 for dynamically convex contact manifolds. This talk will highlight our construction of a non-equivariant version via domain dependent almost complex structures yielding a homological contact invariant which is expected to be isomorphic to SH^+ under suitable assumptions. By making use of family Floer theory we obtain an S^1-equivariant theory defined over Z coefficients, which when tensored with Q yields cylindrical contact homology, now with the guarantee of well-definedness and invariance.