The first change of note is the addition of Gender Based Evolution. In diamond & Pearl, several Pokémon evolve into their evolution based on Gender. For example Combee only evolves into Vespiquen if its female, and considering that Combee's are 87.5% Male, it is a feat indeed. Below are the Pokémon that evolve and the method they evolve with:

Base No.	Pic	Base Name	Method	Final No.	Pic	Final Name
#412		Burmy	Lv. 20 ♀	#413		Wormadam
#412		Burmy	Lv. 20 ♂	#414		Mothim
#415		Combee	Lv. 25 ♀	#416		Vespiquen

A New Concept Discovered is the ability to make a Pokémon hold an item and level it up in order for it to evolve. The Pokémon MUST hold the item in order evolve and some are even time Specific:

Base No.	Pic	Base Name	Method	Final No.	Pic	Final Name
#207		Gligar	Razor Fang @	#472		Gliscor
#215		Sneasel	Razor Claw @	#461		Weavile
#440		Happiny	Oval Stone @	#113		Chansey

Base No.	Pic	Base Name	Method	Final No.	Pic	Final Name
#082		Magneton	Mt. Coronet Range	#462		Magnezone
#133		Eevee	Moss Rock in Eterna Forest	#470		Leafeon
#133		Eevee	Ice Rock in Route 217	#471		Glaceon
#299		Nosepass	Mt. Coronet Range	#476		Probopass

A fair few Pokémon evolve simply because they know an attack, an attack that exists in the moveset. Once the Pokémon learns the attack, if you level them up, they should evolve. However if you get rid of the attack before they evolve, they will NOT evolve:

Base No.	Pic	Base Name	Method	Final No.	Pic	Final Name
#108		Lickitung	Rollout Known	#463		Lickilicky
#114		Tangela	AncientPower Known	#465		Tangrowth
#190		Aipom	Double Attack Known	#424		Ambipom
#193		Yanma	AncientPower Known	#469		Yanmega
#221		Piloswine	AncientPower Known	#473		Mamoswine
#438		Bonsly	Mimic Known	#185		Sudowoodo
#439		Mime Jr.	Mimic Known	#122		Mr. Mime

A one off Pokémon Evolution method is requiring another Pokémon on your team. When you have the Pokémon on your team, the main Pokémon will evolve when it levels up. You will not lose your other Pokémon:

Base No.	Pic	Base Name	Method	Final No.	Pic	Final Name
#458		Mantyke	#223 Remoraid	#226		Mantine

While it is not a new concept, it utilises new items that you may just simply look at and disregard. Simply attach the items to the Pokémon and trade them with your friends:

Base No.	Pic	Base Name	Method	Final No.	Pic	Final Name
#112		Rhydon	Protector	#464		Rhyperior
#125		Electabuzz	Electrizer	#466		Electivire
#126		Magmar	Magmarizer	#467		Magmortar
#233		Porygon2	Dubious Disc	#474		Porygon-Z
#356		Dusclops	Reaper Cloth	#477		Dusknoir

Another not new concept, but requiring new items, there are several new stones. These stones will only work on these Pokémon, one of which only works on Pokémon of a certain Gender:

Base No.	Pic	Base Name	Method	Final No.	Pic	Final Name
#176		Togetic	Shiny Stone	#468		Togekiss
#315		Roselia	Shiny Stone	#407		Roserade
#198		Murkrow	Dusk Stone	#430		Honchkrow
#200		Misdreavus	Dusk Stone	#429		Mismagius
#281		Kirlia	♂ w/ Dawn Stone	#475		Gallade
#361		Snorunt	♀ w/ Dawn Stone	#478		Froslass

Although not a new concept, it is a concept that was brought back after not really existing for the 3rd Generation. Now many Pokémon have the time based Happiness Evolutions. Some Daytime, Some Night Time:

Base No.	Pic	Base Name	Method	Final No.	Pic	Final Name
#406		Budew	Happiness @	#315		Roselia
#433		Chingling	Happiness @	#358		Chimecho
#447		Riolu	Happiness @	#448		Lucario