  In this review, we explain recent progress made in the Babcock-Leighton
dynamo models for the Sun, which have been most successful to explain various
properties of the solar cycle. In general, these models are 2D axisymmetric and
the mean-field dynamo equations are solved in the meriodional plane of the Sun.
Various physical processes (e.g., magnetic buoyancy and Babcock-Leighton
mechanism) involved in these models are inherently 3D process and could not be
modeled properly in a 2D framework. After pointing out limitations of 2D models
(e.g., Mean-field Babcock-Leighton dynamo models and Surface Flux Transport
models), we describe recently developed next-generation 3D dynamo models that
implement more sophisticated flux emergence algorithm of buoyant flux tube rise
through the convection zone and capture Babcock-Leighton process more
realistically than previous 2D models. The detailed results from these 3D
dynamo models including surface flux transport counterpart are presented. We
explain the cycle irregularities that are reproduced in 3D dynamo models by
introducing scattering around the tilt angle only. Some results by assimilating
observed photospheric convective velocity fields into the 3D models are also
discussed, pointing out the wide opportunity that these 3D models hold to
deliver.
