Two molecular beam methods are described for producing anisotropic distributions of rotational angular momentum J or internuclear axis R for diatomic or linear molecules. Both methods exploit the drastic rotational cooling attainable in seeded supersonic expansions and can provide beams with a large fraction of the molecules aligned or oriented. (1) In experiments with I2 seeded in light carrier gases, we obtained marked alignment of J perpendicular to the beam direction, in accord with collisional alignment by bulk gas transport. Under suitable conditions, however, we found J could be aligned parallel to the beam; this and other evidence indicates that anisotropic rotational cooling has a substantial role when the rotational temperature becomes very low. (2) In contradiction to long-held views, we show that R for a linear molecule can be appreciably oriented in an electric field if the molecule is polar or aligned if nonpolar. With sufficient rotational cooling, this becomes feasible with practical field strengths. There is no need to use a focusing field but rather only a short, strong uniform field. The anisotropy of the Stark effect (cos-theta for polar, cos2-theta for nonpolar molecules) allows pinwheeling molecules to be trapped in strongly directional pendulum states. These are formed by hybridization of rotor states with different J values. We present model calculations illustrating this process and nomograms for estimating the attainable anisotropy.