Undoubtedly the height of Incan architecture is the city of Machu Picchu. This city is impressive for more than just its architecture though. The city displays impressive buildings, but also irrigation systems, urban planning, and farmlands clinging to cliffs; in other words a city built around nature using the natural landscape. The Temple of the Sun is perhaps the most impressive structure in the entire city as the stone work and positioning of the building seem to be the pinnacle of Incan architecture.
With the Spanish came new architectural styles and some destruction of earlier buildings. The city of Cuzco suffered the most from Spanish colonization, but other cities also arose, such as Lima, which is primarily in the colonial style.
The colonial style in Peru follows a number of different patterns. From the 1500s into the 1800s, the time of Spanish rule in Peru, a number of European styles were imported from Spain. A couple Renaissance buildings arrived, in particular the Santa Clara Church in Cuzco. Baroque was also popular, in fact much more popular, as Lima is home to the San Francisco Convent and Church of the Compania, both in the style. Arequipa is also home to some of the most authentic Baroque buildings, including the Church of San Agustin and the Church of Santa Rosa.
Most Spanish colonial buildings changed with new influences, but many of the churches and palaces were based on Baroque architecture throughout the colonial period. The cities built under the Spanish also tended to follow traditional Spanish city layouts, which were built on a grid with the town's church and governor's palace in the central square. This layout, along with the Baroque-inspired buildings can be found in the center of numerous Peruvian cities today, most notably in Lima and Arequipa. Lima is truly a Spanish colonial capital architecturally, while Arequipa has more diversity as it generally used local stones and materials to give it a more unique look and feel.
Another excellent city to see colonial Spanish architecture is the city of Trujillo. This city rose in prominence and wealth at the end of Spanish rule so boasts a combination of Spanish architecture as well as more authentic Peruvian architecture still in its infancy (which simply imitated Spanish architecture in most ways). The city is known for its houses, of which there are many that are impressive both inside and out.
Struggling with independence, Peru built mostly in popular European styles in the 1800s, most notably in the neo-Classical style. Again Lima became home to most of these buildings as it was the capital of the newly independent country and the Plaza San Martin is the most impressive of these structures. In a completely opposite direction, the city of Iquitos also rose in prominence during this time, but gained architectural influence from Brazil via the Amazon River. Portuguese tiles decorate the many residences along the river, most of which were built during this time.
In the 1900s and into the 2000s the architecture in Peru has paled in comparison to the structures of its past. None-the-less, new buildings have been built in numerous styles. Many houses have been simple in design and layout, but have used modern building techniques. Modern and post-modern buildings can be found in Lima and other large cities, but not in the numbers these structures are found in many other major world capitals.