Snow can be state-of-the-art chemical technology or good old-fashioned paper bits. Some of the most prestigious theatrical houses still use falling paper, shaken from the catwalks, to simulate floating snowflakes or a heavy blizzard. There are two drawbacks to this effect, which can look perfectly convincing to the audience. First, it leaves a huge mess to clean up between acts or after the show. Secondly, the paper bits have sharp edges -- they are cut paper -- and can cause paper cuts to the actors or stab them in the eye if they don't remember to avoid looking up. Snow machines use a non-toxic chemical mix that sprays out as flakes that can be controlled to pelt or float down. The "snow" can seem to melt in mid-air and just disappear before it hits the ground.
Fog and mist are water -- and water in special misting machines is the cheapest way to control the atmosphere on stage. Theatrical effects companies make machines that send out fine droplets of water so small that it evaporates and the set stays "dry." But there are also fog liquids that create the effect with evaporating chemicals which are safe for actors to breathe and even lay down in, if the part calls for it. School plays might still resort to the time-honored dry ice in a bucket of water. But the cost of theatrical foggers is no longer prohibitive; dry ice is expensive and can be dangerous; it takes a lot of work to produce the fog and control it when using dry ice. Whatever the method, the right lighting enhances the effect of the fog, mist or haze that is produced.
A scrim is a flat sheer curtain that appears opaque when lit from the front and misty and transparent when lit from behind. Scrims can be used to change scenes without moving any sets -- the first scene takes place in front of the scrim, which appears to be a solid wall. Then the light behind the scrim comes up and the upstage scene is revealed. Sometimes the scrim is then raised and the actors from the first scene just walk into the new scene. A scrim can create a ghostly image for a play with spirits or hallucinations. Lighting can make whatever is behind the scrim seem ethereal or slightly distant. A person or object that is backlit behind a scrim will project a shadow on the scrim that can grow larger or smaller depending on how close the light is to the shadow form.
Mary Martin flew across the stage as Peter Pan on Broadway in 1954 with the use of a harness and wire. Mary Poppins flew across the whole audience on Broadway in 2006 (and is still airborne every night), with a harness and wire. Some things never change. The best, tried and true theatrical effect is the belief in magic.