This paper deals with the periodic boundary value problem for nonlinear impulsive functional differential equation $$\left\{\begin{array}{c}{x}^{\text{'}}\left(t\right)=f(t,x\left(t\right),x\left({\alpha }_1\left(t\right)\right),\cdots ,x\left({\alpha }_n\left(t\right)\right))\text{for}\text{a.e.}t\in [0,T],\Delta x\left(t_k\right)=I_k\left(x\left(t_k\right)\right),k=1,\cdots ,m,x\left(0\right)=x\left(T\right).\hfill \end{array}\right.$$ We first present a survey and then obtain new sufficient conditions for the existence of at least one solution by using Mawhin’s continuation theorem. Examples are presented to illustrate the main results.

Let $f:[a,b]\times {ℝ}^{n+1}\to ℝ$ be a Carath’eodory’s function. Let $\left\{t_h\right\}$, with $t_h\in [a,b]$, and $\left\{x_h\right\}$ be two real sequences. In this paper, the family of boundary value problems $$\left\{\begin{array}{c}{x}^{\left(k\right)}=f\left(t,x,x^{\text{'}},...,x^{\left(n\right)}\right)x^{\left(i\right)}\left(t_i\right)=x_i,i=0,1,...,k-1\hfill \end{array}\right.(k=n+1,n+2,n+3,...)$$ is considered. It is proved that these boundary value problems admit at least a solution for each $k\ge \nu$, where $\nu \ge n+1$ is a suitable integer. Some particular cases, obtained by specializing the sequence $\left\{t_h\right\}$, are pointed out. Similar results are also proved for the Picard problem.