This is a very good question that is still ongoing.
Each car battery can be charged and discharged many times before being used, like a mobile phone. But after many years of use, even fully charged these batteries cannot hold the same amount of energy than new ones, and they need to be changed. In some cases, they can be then reused for other purposes, for example for storing energy from renewable energy (ex: solar panels or wind energy).
After this, they can be recycled, but this can be dangerous, as they can explode and emit toxic elements. Also different manufacturers at the moments use different design and shape. This limit the recycling that is possible to do. So in practice, the waste can become a big problem, if action are not taken. At the end however, each type of energy or means of transport that we use changes our environment in some way, and may affect us. The challenge is to choose which one has the more acceptable impact for us.
So i think that electric vehicles are a good idea compared to oil cars, but that at the end, individual cars should be used only in situations when it is not possible to use public transport, walking or cycling. A lot of focus should be made to develop those, if we want to preserve our health and the parts of our environments that matter for us.