When I started this idea to write about monster vision and movement it seemed like an easy idea. It was, at first. Until I started working on the movement part. There is a lot of it, so we should get started.
For simplicity's sake, I am going to skip running, shifting, crawling, and squeezing. Those should be in the PHB, go look it up if you like.
Walk (0-10, 12, none)
Normal movement speed.
Fly (3-10, 12, 14)
The monster takes flight and must move at least two squares each round to remain airborne, and is unable to shift or make opportunity attacks. If knocked prone, the monster crashes.
Clumsy (walk 1, 2, Fly 3-8, 10, 12)
While using a clumsy movement mode, a creature is -4 to attack rolls and all defenses.
Hover (fly 3, 4, 6-9, 10, 12, 14)
If a Monster can hover, it can fly without moving on its turn, as well as shift and make opportunity attacks while airborne.
Max altitude (1,2)
If a monster with an altitude limit flies too high, it crashes at the end of its next turn.
Overland flight (10, 12, 15, 18)
An overland flight speed works like a Fly speed except that it can only be used when only move actions and free actions on that round.
Swim (4-10, 12, 16)
A swim speed allows a monster to move through water without an athletics check.
Teleport (2-8, 10)
When a monster teleports, it moves instantaneously to a place within range and line of sight. The monster doesn't provoke opportunity attacks, and is able to go past obstacles and terain, as long as it does not hinder line of sight. Immobilized or restrained monsters can still teleport, if it is in a physical retraint, another creature's grasp, or an immobilizing effect located in a specific place, then it is no longer immobilized or restrained Otherwise, they are still are immobilized or restrained.
Burrow (2-4, 6, 8)
A monster that can burrow moves through Loose soil at their burrow speed, or through solid stone at half speed. Monsters cannot shift or charge while burrowing.
Tunneling (2-4, 6)
Monsters that tunnel while they burrow leave a tunnel behind them. This creature or creatures smaller than it can use these tunnels without penalty, while creatures of the same size have to squeeze, and larger creatures can't make it through at all.
Climb (2-8, 12)
Climb up a vertical surface without a athletics check, ignores difficult terrain and does not grant combat advantage from climbing.
Spider climb (2-6, 8, 12)
Allows monsters to climb on horizontal surfaces (such as a ceiling)
Terrain walk (Earth 4, 6, Forest 4-6, 8, Ice 6-9, Swamp 4-8)
Ignore certain types of difficult terrain, according to the type of terrain walk they have:
Earth - Rubble, uneven stone, or an earthen construction.
Forest - Part of a tree, underbrush, or some other forest growth.
Ice - Ice or snow.
Swamp - Mud or shallow water.
Monster Ignores difficult terrain, can move through obstacles and other creatures, but must end its movement in an unoccupied square.
Some creatures just can't shift.
Phew, finally got through it. Hope you find it helpful!
If you like this post, leave a comment and I'll be more likely to do some more like it!