Essentially, anything that was once living can be composted. However, some things are easier to compost than others. Composting works best with a mix of nitrogen rich green materials like grass clippings and food scraps and carbon rich, brown materials like leaves and newspaper.
Unless managed very well, animal derived materials like meat and dairy can cause bad odours and attract pests such as rats, birds and flies. Generally, it’s best to limit home composting to just plant derived materials. Most composters prefer to be vegan!