We first review transverse-momentum dependent (TMD) gluon distributions at small $x$ and their relation to unintegrated gluon distributions in the Color Glass Condensate (CGC) theory. We then explore several applications of this connection relevant for studying gluon saturation at small $x$. For instance, based on the equivalence between the TMD factorization approach and the CGC cross section for dijet production in proton-nucleus collisions we show onset of saturation effects in the kinematic region of almost back-to-back jets, and a similar result for the case with an extra soft photon in the final state. We also review the property of non-universality of TMD gluon distributions at small x from a CGC point of view. Using the JIMWLK evolution, we observe different behavior of the distributions at small transverse momenta and a restoration of the universality at high transverse momenta. Finally, we show that a similar connection can be made between generalized transverse-momentum dependent (GTMD) distributions at small $x$ and impact-parameter dependent unintegrated gluon distributions in the CGC theory and we study consequences of having such a relation.