Even if I'm assuming you mean the entirety of the Republic of Venice, and not the city alone, this is a little like asking "What was the state of America in the 19th century". A lot of stuff was going on. This is going to be a long post.

The republic had reached its peak in the 15th century. John Julius Norwich pinpoints the completion of the new (current) Doge's palace in the year 1400 as a convenient start date for the Venetian Renaissance. Over the first half of the century that would come, the Republic reached the height of its glory: shrewd diplomacy had led to the entirety of Northeast Italy, Istria, Crete and Dalmatia to fall under the Republic's rule, while the second half of the century saw the Republic gain of Cyprus in the aftermath of the first Turko-Venetian war, goad Charles VIII to descend into Italy to wreak general havoc by claiming the thrones of Milan and Naples, and see Venice become the sole "Italian" power on the peninsula.

But too much of a good thing is, well, too much of a good thing. The next century would be disastrous for the Republic. Exhausted by her wars with the Turks and alienated by every European power because of her constant diplomatic connivery, by 1508 the Pope Julius II had pulled together the King of France, the Holy Roman Emperor and the King of Aragon, along with most of the minor Italian statelets, in the League of Cambrai for the sole purpose of destroying and humiliating the Republic.

But the absurd thing is that the Republic of Venice beat them all. Not so much because of victory on the field of battle; the Venetian army under Condottiero Bartolomeo D'Aviano (yes, the one from Assassin's Creed) was destroyed as they tried to impede the French from fording the banks of the Adda (what was left evacuated to the safe waters of the lagoon). The Venetian fleet, cornered at the mouth of the river Po, was destroyed by Ferrarese artillery (certainly, the Duchy of Ferrara's finest moment. They then proceeded to do little else for the rest of the war). But even as Padua and Vicenza fell to the Austrians, and Bergamo and Brescia fell to the French, the Venetian diplomatic machine was slowly ticking away behind the scenes, slowly convincing Pope Julius that foreign armies on Italian soil weren't such a good idea after all. The Pope was finally convinced to switch sides when the tide seemed to turn for Venice. First the citizens of Treviso rose up against the invaders chasing them from the city; 700 Venetian infantrymen were sent to man the walls, and the city was retaken. Next, an oxcart "conveniently" broke down on the drawbridge in Padua, allowing twelve Venetian knights commanded by future Doge Andrea Gritti to charge into the city and rile the populace into expelling the invaders. By the time Gritti rounded up enough men to march on Vicenza, he found the city gates open to him, the people also having revolted in favor of the Republic. French tried to siege Padua, but the citizens, invigorated by Venetian reinforcements, did not capitulate. Angry and betrayed, the French turned round and marched on Rome.

The Republic was still crippled, but the war went on, and began to resemble a free-for-all, with the French, Austrians, and Venetians fighting across North Italy in every conceivable combination with various Italian statelets such as the Duchy of Florence and the Duchy of Milan entering and exiting as their rulers changed, were overthrown, imprisoned in battle, or otherwise dropped dead from the exhaustion of keeping up with it all.

The war effectively ended in 1516, with peace signed in 1517. The geographic result was the Status Quo Ante Bellum, but the financial result was disastrous for the Republic. The state was nearly bankrupt. The army was decimated. The navy was at the bottom of the Adriatic. The fertile lands of the Venetian plain were trampled and burnt, and formerly prosperous merchants had been taxed relentlessly; as there was no longer a fleet to protect their trade routes, it would take them years to recover.

The later half of the century saw the Republic sit back lick her wounds. The war of the League of Cambrai was the crippling blow. She had begun her stagnation and eventual decline. Although she had met the Ottoman Empire as an equal in her previous two engagements, by the time they clashed again in 1571 the Republic was the definite underdog. In spite of the oft-touted victory of Lepanto, where the combined forces of Venice, Spain and Genoa defeated the Turks at sea, it couldn't stop the republic from losing Cyprus when peace was signed in 1573.

edit:typos