Akari

Akari puzzles, also called Light Up puzzles, are a type of grid-shading logic puzzle in which solvers must place 'lights' in particular cells within a grid so that clues indicated the number of adjacent lights are satisfied and all cells are either in view of a light or contain a light.

Background
Akari was invented in 2001, and was first published by Nikoli.

Puzzle Application
Akari puzzles are composed of black cells (which may contain clues) and white cells. White cells have the option of either containing a light or being shined upon by a light in the final solution, but the placement of these lights is determined primarily by clued cells. Clued cells contain numbers from 0-4, and are always black, meaning that no clued cell can also contain a light. The numbers contained within clued cells indicate the number of lights in the solution that are directly adjacent to those cells.

When lights begin to be placed, solvers eventually must consider the arrangement of black squares, as a proper solution must have every cell be lit up without any lights falling within the shine of another light. When lights are placed, they shine on every cell horizontally or vertically visible to them, meaning that any cells within sight of a light in this way cannot have another light placed in them, forcing solvers to proceed logically towards the end.

Played Straight

 * - While this puzzle doesn't include clues to start with, the meta aspect of it helps with that..
 * - A variety puzzle, but one with four increasingly-large Akari puzzles to solve. They don't contain any major gimmicks, but if solvers haven't seen them before, it might take them to realize that they're Akari puzzles, since a description of the genre isn't given.

Notable Twists

 * - A triangular take on an Akari puzzle. It notably allows for lights to be in the paths of other lights, and since lights are placed in the corners of rooms and light only travels along the same angled paths that the triangles are made up of, every light ends up illuminating the rooms they're directly next to twice.