Shyvana is easily one of my favorite champs that I've played in League. I love her ability to ult out of nowhere into lane for a quick gank, especially post level 6, where night harvester allows your E ability in dragon form to knock most champs down to half health or lower. She has the ability to change the tide of team fights with her ultimate, and the regular use of her E ability. She scales like a mf and will make the enemy team wish they FF'd at 15. She is extremely underrated in my opinion. I feel that most people don't use her because of her early game weaknesses, and her playstyle. She may be a mostly melee champ, but her E ability makes her much more versatile than others might think. I haven't played her with an AD/Tank build, because I personally love her full AP build, but with her ability to have two very different playstyles as a champion makes her one of the most underrated, if not one of the best junglers you can use in the game right now.

Versatility
No Mana
Wave Clear
Late Game Damage as Human Form
INSANE Late Game Damage as Dragon Form
Team Fight Viability
W Ability Speed Boost
Decently Ranged E Ability

Relatively Squishy (Without Tank Build)
Poor Gank Ability Pre Level 6
Needs Lots of Farm to be Viable
Easily Kited
Fury Mechanic Not Easily Understood by Teammates
Poor Utility
Reliant On Ultimate to be Useful in Team Fights

Passive: Dragonborn

Dragonborn gives Shyvana 5 bonus armor and 5 bonus magic resistance. Additionally, this passive lets her deal damage to dragons. Every drake her team gets gives her . While getting drakes is important for any champ you play, it is important for Shyvana. If the game goes on and by 20 minutes your team still doesn't have a drake, .
Q: Twin Bite

Using Twin Bite makes Shyvana attack twice on her next auto attack, the second attack dealing 20/35/50/65/80% AD. It also is an auto attack reset, so always make sure to auto attack before using Twin Bite to get the most out of this ability. Auto attacks on champs and monsters reduce the cooldown by 0.5 seconds.

In Dragon Form, Twin Bite turns into an AOE attack where she cleaves all units in front of her while granting double Fury. In both human and dragon form, Twin Bite applies on-hit effects.
W: Burnout

Activating Burnout deals magic damage (+0.2 per bonus attack damage) to nearby enemies and gains increased movement speed that decays over time. During the spell duration, each autoattack deals increased damage and increases the duration of Burnout as well (up to a maximum of 4 seconds).

Dragon Form increases the range of Burnout.
E: Flame Breath

Flame Breath is your main damage dealer when playing AP Shyvana. This spell scales greatly with Ability Power and marks all enemies hit. Basic attacks against marked enemies deals additional magic damage equivalent to 3.75% of their maximum health.

In dragon form, Flame Breath explodes upon colliding with an enemy champion or reaching the end of it's path. What's left behind is a flame zone that deals magic damage per second and marks enemies with the same passive.
R: Dragon's Descent

Passive: At level 6, Shyvana's basic attacks grant 2 fury in both human and dragon form. While in human form, fury will generate passively per second.

Active: When activated, Dragon's Descent lunges Shyvana towards a target location. Enemies she collides into take magic damage and are pushed into the direction she's lunging. Upon transformation, Shyvana gains bonus health and attack range. Her dragon size also increases per rank. Fury is lost at a rate of 5 per second, so auto attacking in dragon form will help the duration of Dragon's Descent last longer. Once all fury is lost, she returns back to her normal state.