Recently, I've been having trouble with my camps advancing very far, mainly because I can't get stone. (When I remember to plant stuff, and I don't attack a unicorn.) I think that getting to the "Camp" tier, it takes a farm and saw pit, but what about the third tier? Is there a fourth? I've made it to the third tier on v1.3, but can't in the newest version (1.41) even after building every workshop.
In general the requirements to tier up are: population, number of workshops and production (a rating based on the number of things created in workshops). You also need at least one farm.
The requirements for the different tiers is:
Tier 1 (Camp)
2 workshops, population 20-29, and production > 20
Tier 2 (Settlement)
6 workshops, population 30-39, and production > 100
11 workshops, population 40-59, and production > 500
Population 60-99, and production > 1000
Population 100-199, and production > 3000
Population 200+ and production > 10000
There is a bug in the current version (1.41) that if your population exceeds the range of the next tier before you meet the other requirements, you won't progress to the next tier - so if you are at tier 1 and have population 40 before having enough workshops or production then you can't progress to tier 2 but need to skip straight to tier 3 (or cull your population).