In the 1200s until the 1400s little more was built outside the city of Turkistan, which is home to a number of Uzbek-influenced buildings, although some of these are reconstructions today as many of the originals were torn down.
From this time until the arrival of the Russians in the 1800s and the Soviets in the 1900s little changed or was constructed in a permanent manner. The Soviets though began to force the people to settle as cities were built and expanded. To house the people the Soviets built large communist-styled bloc apartment buildings and factories in huge numbers, while religious buildings were not built due to the Soviets being atheist. Almaty is primarily in the Soviet style.
Since the fall of the Soviet Union in 1991, oddly, the new capital of Astana has become a center for post-modern architecture. The most interesting of these new constructions is the Khan Shatyr which is essentially a giant indoor city. But the building doesn't end there as there are dozens of striking post-modern buildings, which can be spotted from just about anywhere in the city as most are skyscrapers.