At the beginning there was not anything that you can call “a firework”, maybe if you use this word in those ages. 

They could think that you are talking about some kind of craft or blacksmith work that needs fire, but that is not the point, the fireworks were discovered after people found the formulation of what we call the gunpowder and we believe that it was discovered more than 2000 thousand years ago in China. The people use to think that they discover it by mistake, mixing three common kitchen ingredients.

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In these days this element is known as gunpowder widely use in a lot of items like explosive and in old times guns, but in those ages, the Chinese people named that interesting black powder "Huo Yao" ("Fire Chemical") and created it further. This chemical mix was put into the hollow of the bamboo sticks and when they were thrown to fire, producing a reaction between fire and the black powder creating the first “firework”.

One of the most iconic fireworks that we know is the “Hanabi”, is very important and in some countries we already know them (because we see then as big rockets that we fire to the sky). 

but originally they are from Japan, in old ages the were used to ward off evil spirits, These fireworks (Hanabi) have a long history in Japan and are an integral part of Japanese summers. Thousands of shows about this awesome element are very common every year across the country. Normally, during the holidays or special days, usually in July and August, with some of them drawing hundreds of thousands of spectators. For the other way, fireworks are not usually used only to celebrate New Year; they are very common in many celebrations.

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Hanabi (actually “Hanabi” is the Japanese way to say fireworks. 

I use this word for cultural reasons) shells range in size from smaller ones to the world record holding “Yonshakudama”(another kind of Hanabi) shells which are 1.2 meters in diameter and weigh several hundred kilograms. One of the most common is the “star mines”, which their shells are made with spherical shapes that at the same time have a variety of burst patterns. There are a lot of fireworks types including the “Niagara sparklers” that are normally set under bridges to resemble some kind of waterfall, and besides that one, we have shells which burst into familiar shapes for examle, hearts, smiley faces and  many other cartoon characters.

Now, talking about shapes, fireworks have a lot of kinds and models that light up the sky and night with a bunch of colors, forms, and pictures. They make this effects with patterns added when they design the firework. 

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Also when you shoot a firework to the air and it explodes the thing that we see is not a simple explosion, it is very precise chemical prose that starts at the moment that the shell explodes. Normally the “stars” that we see in these events when a firework explodes in the air are the result of the reaction of the chemicals with fire, the shape and position of the stars is together with the colors (created with chemicals too, normally the most difficult creation of colors is with blue and green) that you also see.