Roman ruins: In the 1st century AD, the Romans extended Pannonia province all the way to the Danube in order for the river to serve as the eastern border of the Empire. In 106 AD Emperor Trajan made Aquincum, situated in the northern part of today's Buda (Óbuda), the capital of eastern Pannonia (Pannonia Inferior). In its heyday, Aquincum was a notable city with 40,000 or so inhabitants. The best preserved ruin of this ancient town is the Aquincum Military Amphitheater (location here), a giant 13 thousand capacity complex used for gladiator combats and chariot races. It’s about 25 minutes from downtown Pest by public transport. But you don’t even need to leave downtown to find the underground remains of the Contra-Aquincum (location here), a Roman defense fortification from the 2nd century AD, built to strengthen the Empire’s border. You can see more ancient ruins and learn about the history of this region under the Romans at the Aquincum Museum (location here).

Historical housing stock in the Castle District: The castle area in Buda has had a tumultuous history with innumerable sieges led by Tartars, Ottomans, Habsbugs, and Allied Forces over the centuries. This left few of the original buildings from the 13th century intact, but roaming around these narrow historical streets is an experience in and of itself (location here). Today’s street layouts were formed over 600 years ago, and plenty of buildings still stand on the original medieval structures (look for the landmark protection plaques on the sides of the buildings). The brutal siege to reconquer Buda from the Ottomans in 1686 reduced the castle area to ruins. Subsequent reconstructions lent a baroque facade to most residential buildings that, despite the enormous damage during WWII, remain marvels to behold.

National Museum: The imposing Greek Revival building of the National Museum (location here), completed in 1847 by Mihály Pollack, exudes a feeling of order and calm despite its massive size. The Corinthian columned temple portico and tall doors at the top of broad exterior steps convey the authority of the building that houses an exhaustive history, art, and archeology collection of Hungary. The surrounding garden is currently in a sad state of neglect, but is due for a revival this year.

The city fabric of Pest built during the Austro-Hungarian Empire: Along with Vienna, in 1867 Budapest became the “co-headquarters” of one of Europe’s great powers, the Austro-Hungarian Empire. For the subsequent 50 years (the "golden years of Budapest") the city experienced an unprecedented level of urban and infrastructural development. The Grand Boulevard, Andrássy Avenue, as well as the eye-catchingly consistent revival architecture throughout the city are all the result of systematic city planning during this period.

Miklós Ybl was the best-known and most prolific architect of the time but his finest hour was The Hungarian State Opera House (location here), one of the best examples of renaissance revival architecture, the dominating style of the era. Completed in 1884, the richly-decorated building includes statues of Hungary’s well-known composers (Franz Liszt and Ferenc Erkel), marble columns in the vaulted lobby, and a 1,261 capacity hall with a giant bronze chandelier weighing over 3 tons. The building is considered one of the finest opera houses in the world.

Awe inspiring classical elements are on display at the richly adorned 145m long monumental building of the former Budapest Stock and Commodity Exchange that dominates the stately Liberty Square (Szabadság tér). At the time of its completion in 1907 this gigantic building was one of the largest stock exchanges in Europe. The trading floors with 18m high ceilings were on the two sides of the symmetrical building. Not in need of such a detestable capitalist institution, the communist regime expediently shut down the stock exchange in 1948, which has been in a sad state of disrepair since the Hungarian National Television moved out in 2007. Plans for a gut renovation periodically emerge, but construction works are painfully slow to commence.

The largest building in Hungary, the House of Parliament (location here), is a turn-of-the-century giant Gothic Revival complex stretching imposingly along the Danube river. After 17 years of construction, the seat of the Hungarian national assembly was finally completed in 1902 with 691 rooms, a total of 20km length of staircases, and a 96m tall dome. The rich iconography on the beautifully restored Hungarian limestone façade depicts the coat of arms of major cities and counties of the Austro-Hungarian Empire. Parts of the building are open for visitors, including the hall that once housed the Upper House.

Hungarian Art Nouveau: Ödön Lechner, the “Gaudi of Hungary”, was a pioneer architect who founded Hungary's unique style of Art Nouveau. His buildings using motifs taken from Hungarian folk art are found across Budapest. One of Lechner's masterpieces is the Postal Savings Bank (location here) from 1902, nestled on a quite side street at Liberty Square next to the American embassy. His fluid shapes, rich ceramic decoration, bright green tilework supplied by the renowned Zsolnay porcelain maker, and curvilinear wrought-iron entrances gave birth to a new architectural style in Hungary. Check out also the building of the Museum of Applied Arts (location here) and that of the Geological Museum (location here) to marvel at more of Lechner’s genius.

Another important, though lesser known figure of Hungarian art nouveau architecture was Béla Lajta. A student of Lechner, he took his master's national style into new, often visionary directions. The Parisiana (1908, location) and the Rózsavölgyi house (1912, location) bear distinct Art Deco and early modernist characteristics, well ahead of the widespread popularity of these styles.

Modernism: Following WWI, modernist architecture left a distinctive mark on the architectural landscape of Budapest. In fact, several well-known figures of the Bauhaus school were Hungarians (Marcel Breuer, László Moholy-Nagy), although many of them later migrated to the United States.

The highest concentration of modernist buildings can be found along Pozsonyi út in Újlipótváros (location here), with the most lavish under Pozsonyi út 38. But fans of this style should certainly go see the residential homes along Napraforgó Street in Buda, where concrete constructions, modular structures, and flat roofs dominate the street view (location here). This row of modernist buildings was the result of a progressive government decree in the 1930s that commissioned architects to build affordable housing in the leading style of the day.

My favorite building of this era is the residential home designed in 1932 by Farkas Molnár, a graduate of Bauhaus, which radiates a sense of luxurious minimalism (the building is nestled in the side of a hill and difficult to approach, the best view is from the memorial at Apor Vilmost Square).

Contemporary: For architecture buffs interested in contemporary constructions, I've three specific recommendations. Bear in mind that many downtown neighborhoods or buildings are under landmark protection, so architects need to walk a fine line between preserving the old (be it the fabric of a street or the facade of a building) and creating something that meets the expectations of the 21st century.

The recently completed building of the prestigious Central European University (location here) did exactly this. The playfully indented facade, elliptical concrete staircase, steep glass-steel roof planes, as well as the quality and richness of details are marvels to behold. The building, with a café on the ground floor, is open for all to see.

The harmonious combination of old and new is on display at the CET Building located along the Danube river. The building complex is a cultural and commercial space consisting of a set of gracefully restored warehouses and a whale-shaped steel-and-glass modern wing inserted in-between.

The new metro line #4 appears to be a commercial failure. Completed way over time and budget, it does not generate nearly the passenger traffic it was projected to. However, the design of the stations are at the forefront of contemporary Hungarian architecture. A crisscross system of exposed concrete beams, playful lighting solutions, and a creative use of natural light lend a distinctively 21st century feel to these spacious platforms. The gracefully minimalist design along with the disability-inclusive infrastructure stand in wild contrast to the city’s otherwise outdated socialist-era subway stations (at the Kálvin tér station you can compare and contrast the two). The Fővám tér and Szent Gellért tér stations (see location), adorned with colorful mosaics, won the highly prestigious Architizer A+ Award in 2014.