We did not just have ice ages on Earth we are in one right now, the Quaternary glaciation started 2.58 million years ago and is ongoing. A ice age is when there is are constant ice sheets. So we just need to observe Earth right now and we can see we are in an ice age.
During ice ages, there is glacial periods the climate is even colder and the ice sheets grow. This is what most people think about when you say ice age, The last one that is just called the Last Glacial Maximum was 26,000-20,000 years ago and a large part of North America, Europe, and Asia was covered by ice sheet, it resulted in lower water level all over the world.
There have been at least eight glacial periods during the last 740,000 years. So with the more common interpretation if ice age there have bee lost more than 5. We know the temperature and climate in multiple ways, one way it to look at CO2 level is bubbles trapped in ice in continental ice sheets. Here is one graph of the levels for the last 800,000 years https://en.wikipedia.org/wiki/Glacial_period#/media/File:Co2_glacial_cycles_800k.png
The period between a glacial period is called an interglacial period. We are in right now, is is called the Holocene and started about 11,700 years ago.
So we are in an ice age and in an interglacial period. There is ice sheet on earth but that does not cover as large areas as during the cooler part of an ice age.
If you live where there have been glacies in the last glacial periods the effect of it is quite clear in the landscape. The bedrock is quite smooth because it was ground down by the glaciers and you can see https://en.wikipedia.org/wiki/Glacial_striation on the bedrock. We see the same marks on bedrock that in modern times was covered by glaciers.
There are https://en.wikipedia.org/wiki/Esker which are long ridges of sand and gravel that are from in front of a glacier. The ice age did not just end with glaciers retreating, they moved forward during winters, and there is the shorter colder periods when they grew a bit. There are https://en.wikipedia.org/wiki/Terminal_moraine formed in process like this that are 100 kilometers in length. They are formed by modern-day glaciers too but on a smaller scale.
You also have the https://en.wikipedia.org/wiki/Post-glacial_rebound Ice sheets are heavy and pushed down the ground. When the ice retreated the ground rebounded and moved up. The ground moves slowly and it does not stop in some places. It rises at rates of almost 2cm/year in some places.
Where I live it is just below 1 cm/year. That is almost a meter per century and it has a clear effect on the environment. It is fast enough that you can see the change in your lifetime. Small wharfs built for cottages on the coast and islands 100 years ago are today on dry land. There are former shingle beaches on the top of small mountains, the higher one close to me is 180 meters above the current day sea level
The city moved in the 17th century because the water level in the harbor decreased so it could no longer be used. It is not a case of sedimentation, you same effect with bedrock that rises above sea level
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