Well, first off - my apologies if self answers are considered bad. Most of my study earlier stopped by 2-3 years and if at all there is, it is very limited exploration [ See wiki, nidcd, nncc ]
More sources i got later: rising children, child development. Again, i am really not sure of other sources.
Basically, here is how i have gathered stuff, and there is some which is partly added i have observed around in my and other kids. I may be completely wrong - nevertheless, here it is!
1. Understanding actions:
from basic instructions - "give me water, put that shoes" etc. to more complex instructions like, find the largest ball from there and put it in most fitting basket here.
The same way, child grows to understand puzzle solving, understanding the relationship on different scores and levels and then they understand the notion of competitive winning.
broadly they develop simple to complex understanding of things - for example as early as 1 year my kid learnt that pressing the specific key will switch on light. From there, they understand more complex phenomena around her/his world and establish cause and effect relationship. for example, operating power on-off button to switching channels in TV and then knowing which channel will get their favorite channels is a simple to complex learning
2. Language development
Simple to complex sentences. Use adjectives. Understand distinction between noun and verb and realizes that verbs are related to actions.
understand opposites, relations like - big/bigger/biggest.
understand and answers questions on - WHO, WHAT, WHERE, WHICH etc.
Ability to do longer conversation - like replying on phone, reply of reply to lengthen it towards some motive,
answer an abstract questions:
3. Sense of time
in the beginning - they decipher day vs. night. Later distinguish other day parts.
Primary causality: Post this, they being to have basic understanding of what happend before or after.
Understand wall clock time.
Understand week days and notion of what days, month, year elapsed would really mean.
4. Visualization
[I am not sure of this - but this will be part of one of the other sections]
About 18 month+ kid can remember a scene setting scene before but not right in font of the eye.
Ability to draw and depict objects and scenes based on pictures, cartoons and other such imaginary sources rather than real world. For example, kids can identify and relate a tiger from a picture as well as a 3D model (toy) and a cartoon tiger as well as a real tiger in zoo.
Can express the entire scene - this is what all i saw in the garden and then from there - express complex phenomenon - this happend - then this happened and then etc.
5. Social Awareness
interaction with other kids, understand their actions and react to them.
play games for enjoyment sake initially which later evolve in relative comparison and competitive spirit.
develops, liking- disliking, develops basic trust by way of preferring someone by default, understanding of what will hurt or please others, learns to manipulate response for objectives (pleases someone to grab a chocolate).
internalize behavioral manners and code of conduct, understands seniority of people, learns to influence or persuade or bargain with people.
6. Math and logical reasoning
I feel this is very very tightly governed by what is explicitly taught in school. Even if there is a capability in children to learn them on their own - but schools syllabus is more or less primarily driving them then their natural discovery. Thoguh it is a great surprise to me how it works. the play school of my kid tried to teach him counting. Most kid would do that by end of 2 - my kid was not able to grab that concept till 2 & half - but suddenly one fine day he just begun to count! So i don't really know how that works.
Same applies to reading and writing i guess.