The theory of conforming finite element exterior calculus has been well developed, and the research has now reached a point where extension is appropriate to nonconforming methods, of which some progress will be reported. This talk will firstly present a unified family of consistent nonconforming finite element spaces for $H\Lambda^k$ in $\mathbb{R}^n$, $n\geqslant 1$, $0\leqslant k\leqslant n$. The spaces employ piecewise Whitney forms as shape functions, based on which discrete de Rham complexes with commutative diagrams are established. A theory of nonconforming finite element exterior calculus is then given. Its combination with the classical conforming one helps reconstructed some structural properties at discrete level, which can not be done by the conforming FEEC alone. Finally, based on these new spaces and the new construction approach, new primal schemes are introduced for the Hodge Laplace problem, for which reasonable conforming primal discretizations are impossible to construct.