Gun powder saw its introduction in Europe in late 13th and early 14th century and in the first canons came on the market and battlefield around 1300-30s. They were massive machines, shooting stone rounds and needed often half a day to be prepared, shot and cool down before the next shot could be made. The effect bepended on luck as often the stone round broke on inpact dealing little damage. So at first they were no actual alternative for siege engines. However, we must understand that siege engines were, expensive. In labour, materials and money to pay the engineer which build them. They often were craftsmen that traveld around from war to war selling thier machines, which they built on location, to them that could pay. That group was small, really small. Only Emperors, kings and some grant duke could pay for such machines and often after the siege the big ones were abandoned/burned only taking essential elements like metal parts or ropes. As transporting the whole construction was tremendous endavour, it was easier to build a new one at next siege, but also expansive. So in most sieges none such engines were used. The simple tools like ladders or burning the gate were used. Those lords that had mines in thier realms often used the miners as sappers, which were handsomly paid for it. Canons were long time in the category of being only a toy for richest lords and although, as seen with Edward III and his use of canons, they were less able than other siege engines, you could take them with you after the siege which made them cheaper and quicker to opperate at the next siege. By the late 14th century they became more frequent. The use of Bronze for cannon and iron for ball made them more effective. First carriages made the transportation and on field positioning easier. By 1411 we see still use of trebuchets in Bohemia, by the king of hungary that invade his brothers land. Yet, by 1420s with the hussite rebelion we see the first effective use of gunpowder weapons, (gun and handweapon) during sieges and battlefield. The sieges engine loses in this period completly it position as wall breaker to the cannon. As of the siege engines which purpose is to climb walls or break gates, they will continued to be used till in the 16th and even in some case till.17th century, yet less frequent. The last big use of siege engines was the siege of Constantinople of 1453. Yet it was won buy the the cannon. At the time of the fall Constantinople cannons might have suppersede siege engines in thier ability, but were still not common in europe as were the siege engines. Yet, it was the siege of Constantinople and the turkish cannons that called in thier age. In the second half of the 15th century cannons were seen in every army becoming the tool to crack walls and became even more common as siege engines ever where (exceptation of Roman time, which was achieved in the late 17th century).