I do not like the term of race. For me a race is a category in biology that is under the species (species being the category of individuals who can mate and have offspring together - so there is a species of horses, cats, Grey squirrels etc) and is defined by a breeding standard.

Humans have differences that are partly genetic and partly cultural. For humans with a mix of these differences I prefer the term "ethnic".

Why? Race only describes genetic differences and in general, humans are genetically very very similar. Two individuals from one "race" can have a much bigger genetic variety than the average variety between two "races".

It all started in Africa (well it does for most contemporary scientists): In most places now, people are that much genetically mixed, that no-one can tell to what "race" they might belong. In good old Europe it is the mix of original inhabitants, Romans, Central Asians coming during the time of migrations (ca. 500 A.C.) and everything that happened in history after that.
In the US, some Central Asians crossing the land bridge between Asia and America 35.000 years ago added to that mix coming over after 1492.

Ethnically I'm a European, German variety