There has been some work on the use of technology by toddlers (for example, this paper). By and large, there are some advantages to the use of some of these technologies by children. For example, even two-year-old children started collaborating more and working in concert even when they were using their personal iPads (see link above). But there are other disadvantages that might arise through technology use such as access to violence (source).
What kind of devices do/did you allow your toddlers to use? If a toddler wants to use an iPad that the parents own, how were they allowed to use the iPad? Are there any apps that would be interesting/useful for them when using such technology?