Nonlinear transport phenomena induced by the chiral anomaly are explored within a 4D field theory defined holographically as $U(1)_V\times\U(1)_A$ Maxwell-Chern-Simons theory in Schwarzschild-$AdS_5$. The present study goes along two complementary directions. In the first part [1], in presence of external electromagnetic fields, a general form of vector and axial currents is derived. Within the gradient expansion up to third order, we analytically compute all (over 50) transport coefficients. A wealth of new phenomena beyond the Chiral Magnetic and Chiral Separation Effects are discovered. Particularly, the charge diffusion constant and dispersion relation of Chiral Magnetic Wave are found to receive anomaly-induced non-linear corrections due to e/m background fields. Furthermore, there emerges a new gapless mode, which we refer to as {\it Chiral Hall Density Wave}, propagating along the background Poynting vector. In the second part [2], gradient resummation is performed for nonlinear chiral transports. In presence of weak constant background electromagnetic fields, the constitutive relations for vector and axial currents, resummed to all orders in the gradients of charge densities, are encoded in nine momenta-dependent transport coefficient functions (TCFs). These TCFs are first calculated analytically up to third order in gradient expansion, and then evaluated numerically beyond the hydrodynamic limit. ( [1] arXiv: 1807.08467 - [2] arXiv: 1807.11908)