Like every New Generation of Pokemon, the Seventh Generation brings with it a number of new ways to evolve certain Pokemon. These can be based on Level, Stats, Gender, Knowing Certain Attacks, or even Location of Evolution. Sometimes, especially within thee games of this generation, the Time of day in-game usually plays a role too.
New Level Up Evolution Methods
Alolan Rattata INTO Alolan Raticate: Level 20 (Nighttime)
Cubone INTO Alolan Marowak: Level 28 (Nighttime)
Yungoos INTO Gumshoos: Level 20 (Daytime)
Rockruff INTO Midday Lycanroc: Level 25 in Pokemon Sun (Daytime)
Rockruff INTO Midnight Lycanroc: Level 25 in Poemon Moon (Nighttime)
Salandit INTO Salazzle: Level 33 (Female Only)
Cosmoem INTO Solgaleo: Level 53 in Pokemon Sun
Cosmoem INTO Lunala: Level 53 in Pokemon Moon
New Attack Based Evolution Methods
Steenee INTO Tsareena: Level Up Knowing The Move Stomp
New Evolution Stone Evolution Methods
Alolan Sandshrew INTO Alolan Sandslash: Ice Stone
Alolan Vulpix INTO Alolan Ninetales: Ice Stone
Pikachu INTO Alolan Raichu: Thunder Stone
Exeggcute INTO Alolan Exeggutor: Leaf Stone
New Location Based Evolution Methods
Magneton INTO Magnezone: Level Up At Vast Poni Canyon
Eevee INTO Leafeon: Level Up At Lush Jungle (Moss Rock)
Eevee INTO Glaceon: Level Up At Mount Lanakila (Icy Rock)
Nosepass INTO Probopass: Level Up At Vast Poni Canyon
Charjabug Into Vikavolt: Level Up At Vast Poni Canyon
Crabrawler INTO Crabominable: Level Up At Mount Lanakila