  We extend the theory of Vassiliev (or finite type) invariants for knots to
knotoids using two different approaches. Firstly, we take closures on knotoids
to obtain knots and we use the Vassiliev invariants for knots, proving that
these are knotoid isotopy invariant. Secondly, we define finite type invariants
directly on knotoids, by extending knotoid invariants to singular knotoid
invariants via the Vassiliev skein relation. Then, for spherical knotoids we
show that there are non-trivial type-1 invariants, in contrast with classical
knot theory where type-1 invariants vanish. We give a complete theory of type-1
invariants for spherical knotoids, by classifying linear chord diagrams of
order one, and we present examples arising from the affine index polynomial and
the extended bracket polynomial.
