The first mugs were invented in the Neolithic Period, dating back to 10000 BC. But those were made of skulls, when we think of coffee mugs, we think of a variety of types. Blacksmiths would later start making metal mugs, or even lead mugs during 3000 BC, these were difficult due to how scalding hot or poisonous they were. Later in 850 BC, an Ethiopian farmer would discover coffee beans eventually leading to the spread of the drink we know today.
Porcelain was then invented in 600 CE China, making for more heat friendly and portable drinkwear. This would also allow for cool designs to be incorporated into mugs. Mugs were also discovered in Ancestral Pueblo from 1000CE to 1280CE, showing how universal the design was. The modern coffee mug was invented in the early 1800s, being really popularized when the Victor Insulator Company in 1945 America rose to prominence with the rise of American diner culture and World War II, as the mugs were made more durable for the war. leading to the modern coffee mug we know today.
Additionally, espresso cups were made by an Italian inventor in the early 19th century and 20th century by Luigi Tazzini and the modern travel mug can be traced to the invention of the vacuum flask in 1904, by Sir James Dewar. This technology was used for chemical experiments, so two glassblowers from Germany took this tech and named it the thermos in 1904. The thermos would later become generalized to mean anything with vacuum flask properties. Later in the 1980s and 1990s, the modern travel mug would become popular, along with the invention of the cupholder in 1953. In 1997, Thermos would introduce their insulated travel mug line, associating travel mugs with high quality and luxury, as well as rising their sales.