In quantum interferometry, it is vital to control and utilize nonlinear interactions for achieving high-precision measurements. Attribute to their long coherent time and high controllability, ultracold atoms including Bose condensed atoms have been widely used for implementing quantum interferometry. Here, we review the recent progresses in theoretical studies of quantum interferometry with Bose condensed atoms. In particular, we focus on the nonlinear phenomena induced by the atom-atom interaction and how to control and utilize these nonlinear phenomena. Under the mean-field description, due to the atom-atom interaction, matter-wave solitons appear in the interference patterns, and macroscopic quantum self-trapping exists in the Bose-Josephson junctions. Under the many-body description, the atom-atom interaction can generate non-classical entanglement, which may be utilized to achieve high-precision measurements beyond the standard quantum limit.