  In the present paper we focus on the problem of the existence of strange
pseudohyperbolic attractors for three-dimensional diffeomorphisms. Such
attractors are genuine strange attractors in that sense that each orbit in the
attractor has a positive maximal Lyapunov exponents and this property is
robust, i.e. it holds for all close systems. We restrict attention to the study
of pseudohyperbolic attractors that contain only one fixed point. Then we show
that three-dimensional maps may have only 5 different types of such attractors,
which we call the discrete Lorenz, figure-8, double-figure-8, super-figure-8,
and super-Lorenz attractors. We find the first four types of attractors in
three-dimensional generalized H\'enon maps of form $\bar x = y, \; \bar y = z,
\; \bar z = Bx + Az + Cy + g(y,z)$, where $A,B$ and $C$ are parameters ($B$ is
the Jacobian) and $g(0,0) = g^\prime(0,0) =0$.
