We describe some properties of braided generalizations of Thompson's groups, introduced by Brin and Dehornoy. We give slightly different characterizations of the braided Thompson's groups $BV$ and $\widehat{BV}$ which lead to natural presentations which emphasize one of their subgroup-containment properties. We consider pure braided versions of Thompson's group $F$. These groups, $BF$ and $\widehat{BF}$, are subgroups of the braided versions of Thompson's group $V$. Unlike $V$, elements of $F$ are order-preserving self-maps of the interval and we use pure braids together with elements of $F$ thus again preserving order. We define these pure braided groups, give normal forms for elements, and construct infinite and finite presentations of these groups.