There are many vehicles in warframe ranging from battle robots that can be used on the surface of a planet to "jetpacks" that can be used in the vaccum of space to in-atmosphere and the crushing depths of the ocean. So far there are 3 vehicles able to be used, the archwings, k-drives, and necramechs.
The Archwing is an all-environment flight system of Orokin design used by a Tenno to fly and engage in combat in space, offering a potent mix of firepower and mobility to engage spaceborne enemies. Archwing missions take place on a three-dimensional plane, offering nearly complete freedom of movement in all directions. Though intended for space use, the Archwing also has the ability to engage in both atmospheric and underwater combat.
There are 5 archwings in the game. The Odonata and the Odonata which is the first and most balanced of the archwings with offensive and supportive abilites. The Itzal which is the fastes of the 5 with more offensive abilites. The Elytron which is the slowest but the hardest hitting with all offensive abilites. The Amesha which is another fast archwing but with all supportive abilities. Odonata and Odonata Prime pictures below.
The archwings also have their own set of weapons. The archgun and the arch-melee. The archgun can be used in normal missions after recieving the archgun launcher from the Profit Taker fight.
K-drives are hoverboards that can be built on the Orb Vallis. They are the only modular vehicle in the game. They can be modded to change jump height, launch speed and other things. On The Cambion Drift there are massive bugs you can ride called Velocipods that function similarly to K-drives. Velocipod pictured below.
Necramechs are Entrati war machines encountered on the ruins of Cambion Drift. They are heavily armored bipedal war machines built during a war as a predecessor to Warframes, though they were far less intelligent. The Tenno are capable of accessing these relics using their Transference, and can deploy them in the openworlds and railjack missions. There are 2 necramechs in game, Voidrig and Bonewidow. The Voidrig necramech next to Excalibur.
Railjacks are large Orokin-era interceptor spacecraft used by the Tenno. These formidable spacecraft feature a plethora of weaponry and defensive systems that allow them to face even large capital ships head-on in direct combat, as well as a "Void engine" propulsion system that allows them to travel independently of the Solar Rail Network. A picture of the railjack in its docked state in the Orb Vallis from Tennocon 2018.
This one needs quite a bit of explaining. The Duviri Paradox is believed to be the next open world for warframe and in this trailer the Tenno is ripped out of their warframe and is either transported here or had a vision of this. In this the Tenno is being chased by this unknown figure after looking at the crashsite of the Zariman Ten Zero, a ship lost in the Void. The Tenno managed to take out this unknown figure and is next seen riding the unknown figure's horse towards the ship. I believe the horse will be added as a vehicle becasue in every openworl a new vehciel has been added. The Plains of Eidolon added archwing launchers, the Orb Vallis added K-drives, and the Cambion Drift added necramechs.