The author describes some of the recent developments in the application of harmonic analysis to nonlinear dispersive equations \[ u_t= iP(\nabla_x)u+ F(u)\;(t\in\mathbb{R},\;x\in\mathbb{R}^n) \] with initial data \(u(0,x)= u_0(x)\), where \(P(\nabla_x)\) is a differential operator with constant coefficients, \(F(u)\) represents nonlinearity. Two important problems are considered. The first one is the problem of the minimal regularity of the data \(u_0(x)\), which guarantees that the initial value problem for the nonlinear dispersive equations is well-posed. The notion of well-posedness includes existence, uniqueness and persistence. The main idea is illustrated by the generalized KdV equation \[ u_t+ u_{xxx}+ u^ku_x= 0\;(t,x\in \mathbb{R},\;k\in\mathbb{Z}^+),\;u(0,x)= u_0(x). \] The second problem is the existence and uniqueness to the initial value problem for some dispersive models for which classical approaches cannot be applied.