Creation of ultracold atomic ensembles triggered the studies of fundamental aspects of quantum mechanics. In manybody systems, the ability to generate non-classical correlations between atoms opened the possibility for their practical applications in non-trivial ways, for example in quantum computation or quantum-enhanced metrology. However, before the implementation stage, we must first make sure that the entanglement is present in the system, which is often a difficult task. In this talk, I will describe experiments that were conducted to verify existence of non-classical correlations in ultracold atomic systems. I will describe criterions by which the nonclassicality was certified, and how these measures are related to interferometry. In a special class of experiments, two groups of atoms are produced in which the non-classicality stems from indistinguishability between pairs of particles. I will show how these correlated pairs of atoms are generated, and how they can be used for quantum-enhanced interferometry or fundamental tests of quantum mechanics, like the violation of Bell's inequality.