The Thunder Spears are based off of technology that had been preserved in secret by the Interior Police, despite their orders to wipe out any sign of technological innovation. This technology was adapted to design a new special weapon for use against the Armored Titan. It works in a similar fashion as the Anti-Personnel omni-directional mobility gear's guns and hooks, but with a strong spear loaded with explosives designed to shatter armor.
These weapons work as a two-stage rocket: an initial charge launches the projectile by pressing a special trigger in the handle of the device. The projectile, connected by a string to the main engine, is launched with enough power to penetrate hardened Titan skin. When that string is cut, a safety pin is pulled and the second charge is activated. This causes a tremendous explosion which makes the projectile penetrate even more into the target. The time taken for the second charge to fuse and cause explosion is near instant, but nevertheless enough for users of the Vertical maneuvering equipment to move away safely. 
Usually one is carried on each arm, but up to four can be carried with proper modification to the mobility gear, making eight in total.
Usage and limitations
The Thunder Spears are a weapon which enables a human team to efficiently launch a surprise attack against the Armored Titan. But this weapon plays the role of a double-edged sword, as it is a danger to its user as well as the Titan. So much so, that it is only useful in a specific type of situation where after use, immediate retreat to close structures via ODM gear is possible. Without a proper surrounding, the user is easily liable to get caught in the explosion. While it is also capable of damaging other types of Titans, it was designed solely to kill Reiner, the Armored Titan.
Later, they were used as anti-Titan and anti-fortification weapons against the War Hammer Titan, and the Anti-Titan Artillery that the Marleyan military acquired after their war with the Mid-East Allied Forces.
In preparation for defeating the Armored Titan, Squad Levi did not have much time to train, but Hange carefully placed their troops so that they would be in an optimal position to attack. It is a maneuver that requires three successive attacks: the first to blind the target, the second to break the protective shell, and the third one to kill.
Hange Zoë has the Corps of Engineers develop the Thunder Spears, using technology uncovered following the coup d'état. Designed as a weapon to combat the Armored Titan, Hange displays the performance of the spear to Scout Regiment soldiers.
In the battle in Shiganshina District, the members of Fourth Squad and the Special Operations Squad surround the Armored Titan in its battle, barraging it with explosives and blowing through its armor to detonate its nape.
Later in the battle, part of the Special Operations Squad combat the Colossal Titan. While Jean Kirschtein, Sasha Braus, and Conny Springer attempt to divert its attention, Mikasa Ackermann uses Thunder Spears to attempt to hit its nape from behind. However, the transparency of the plan leads to the attack being countered with a burst of steam. The shrapnel hits Mikasa, creating a shallow wound.
The same part of Squad Levi later use their four remaining Thunder Spears to combat Reiner, following his return to the conflict. Mikasa uses the first spear to break the Armored Titan's leg. Sasha and Conny try to use their spears to break Reiner's jaw, though Sasha misses due to Reiner's counterattack. Hange returns to the battle, using their spear to blow the second hinge of the Titan's jaw, allowing Mikasa to fire the final spear through its mouth, blowing Reiner directly out of his Titan's nape.
Four years later in the Raid on Liberio, the Scout Regiment employ Thunder Spears to counter Marleyan personnel, as part of their urban warfare tactic. The Thunder Spears are used in conjunction with the corps modified Anti-Personnel omni-directional mobility gear, to destroy anti-Titan artillery set up as defense in the internment zone. Mikasa assists Eren Jaeger against the War Hammer Titan, firing numerous Thunder Spears at the Titan at once, to sufficiently destroy its nape. When this is not enough, due to the mechanics of the War Hammer Titan, Mikasa distracts the Titan by engaging it using her Thunder Spears. She later tries to destroy its pilot's crystal, though the explosion proves unsuccessful.
After the Raid on Liberio, the Scout Regiment would bring a number of Thunder Spears with them to the Forest of Giant Trees where Zeke Jaeger is being detained. Later, Levi uses several of these to defeat the Beast Titan, using them to destroy the Titan's hardened nape. After dragging Zeke out of the forest, Levi places the tip of another spear inside Zeke's stomach. By wrapping the spear's fuse around his neck, Zeke is stopped from being able to move, lest his insides detonate. Despite this, Zeke goes on to detonate the Thunder Spear, catching Levi in the resulting blast. While the blast mutilates him enough to where he could no longer regenerate his wounds, he instead would end up in the unknown land.