The role-playing genre is one of the most complex and varied genres in gaming. While there are many ways to categorize RPGs, the easiest way to do it is based on combat, and that's where action RPGs ( aka “ARPG”s) shine.
Basic ARPG Definition
Put simply, an action RPG is a role-playing game in which combat occurs in real time in direct response to player inputs. In other words, one button press results in one attack or movement, with little or no delay. This contrasts with other RPG systems in which character actions are limited by a timer, turn order, or navigating a menu.
Subgenres
In the games industry, there have been many approaches to ARPG gameplay and presentation. So from here, I'll break the genre into 3 subgenres. I'll also provide a classic and modern example of each.
Note: Instead of using games industry jargon terms for these subgenres, I've broken down these categories based on how the gameplay feels. However, I've also included examples of analogous, more industry-standard terms for reference.
Clicker (aka “action CRPGs“)
Clicker ARPGs originated on PC and rely on the mouse as the primary form of player input. Click on a spot on the ground to walk there; click on an enemy to attack it. This is a genre that will really put the durability of your gaming mouse to the test! Another hallmark of this subgenre is that the game world is usually presented in a zoomed-out isometric perspective. That being said, some first-person games also fit in this subgenre based on their mechanics.
Note: Many clicker ARPGs have now been adapted to play with a controller for consoles, but the general structure and PC roots will still be apparent.
Classic example: Diablo (1996)

Considering Diablo means “devil” in Spanish, the dark and spooky vibe fits. (Image credit: Gog.com)
This game is such a core part of the ARPG canon that you would be justified in calling this subgenre Diablo-like. Diablo features real-time mouse-based combat, isometric perspective, and most importantly, an irresistible loot collection loop.
Modern example: Torchlight 3 (2020)

Torchlight 3 bucks the trend of dark and serious CRPGs.
While clearly made from the mold of Diablo, the Torchlight series brings its own unique flavor to the subgenre. In Torchlight 3, I appreciate its bright color palette and more unusual options for character classes.
Masher (aka “hack-and-slash RPG”)
Masher ARPGs are essentially the console-oriented cousins of the clicker ARPG. In these games, character movement is handled via the d-pad or analog stick on a controller (or arrow keys on a keyboard). Input method aside, what makes this different from Clicker movement is the directness of it; push Left and your character moves leftward on screen. For combat, button presses produce attacks in whichever direction your character is facing. In general, combat in these games tends to be offense-focused, fast, and frenetic.
Masher ARPGs have varied their presentation throughout the years. In retro games, they are usually either overhead or side-scrolling. In modern games, mashers usually have a third-person behind-the-back perspective.
Note: Many games in the Masher ARPG subgenre come from Japan. So they often get lumped in with JRPGs. However, that's a whole other can of worms.
Classic example: Secret of Mana (1993)

Secret of Mana's party has one player-controlled character and two CPU-controlled characters. (Image credit: Square Enix)
In the SNES classic, Secret of Mana, you can cleave through enemies with an assortment of weapons and elemental spells. At the time of its release, its vibrant pixel art was eye-catching even in the tiny screenshots featured in Nintendo Power.
Modern example: Ys 10 Nordics (2023)

This giant bug is just one of the many enemies that will taste your blade in Ys 10 Nordics.
Since the 1980s, Falcom's Ys series has been a bellwether of the masher ARPG subgenre. Their tradition of fine-tuned action combat and killer music continues to this day with Ys 10 Noridcs.
Dodger (aka “Souls-like”)
At the surface level, a Masher and a Dodger are hard to differentiate. Both can have similar graphical presentation and feature direct movement input. So what makes them different? The need for restraint. In a Masher, you can go all out with your attacks; doing this in a dodger will get you killed very quickly, even by a low-level enemy. Most of your time in combat in this subgenre will be spent on dodging, blocking, or parrying enemy attacks until a brief window of opportunity arises to land a strike of your own. Player characters in this game are often slow-moving and take time to recover between attacks, which makes timing especially crucial.
Classic example: Monster Hunter (2004)

Rathalos will put you in your place if you try to beat him via button-mashing. (Image credit: iMore)
While the origins of this subgenre are often attributed to FromSoft's Demon's Souls / Dark Souls series, its roots go back further than that. Capcom's long-running and immensely popular Monster Hunter series features characters with weighty weapons taking on towering beasts. In most battles, a well-timed dodge-roll is the only thing keeping you from becoming monster chow.
Modern example: Elden Ring (2022)

This monster is attributed to several of my hundreds of deaths in Elden Ring. (Image credit: Steam)
By going to an open-world environment, FromSoft added a whole new layer to their already-beloved action RPG formula. With such a rich world to explore, Elden Ring allowed players to roam freely… and get murdered by horrible creatures in more interesting and varied settings than ever before. It's a combination that proved to be as addictive as it is challenging.
Conclusion
If you like the idea of getting engrossed in the stories and world that RPGs are known to provide, but hate waiting your turn, action RPGs are for you! With so many options in terms of playstyle, tone, and graphical presentation, this genre is bound to offer something that'll capture your imagination without testing your patience.