Judaism is a religion. One can convert to it, but this is usually not easy. Jewish identity is inherited, but has nothing to do with race - there are black Jews and Chinese Jews, for example. The Law of Return was designed to cover all persons who suffered persecution for being Jews during the Holocaust. Next question!
Great Answer, eclectic. It also is not necessarily a religion, but a birthright and a way of life. Most people don't realize that all of the 633 laws that G-d gave the Jews are to enhance their daily lives in obedience to G-d--e.g. that if they adhere to the laws they will live long and have happiness in the covering of Ha Shem. As far as race, I contribute most to help Aliya for the Ethopian Jews. It is truly a blessing to see the happiness and appreciation that they have when they come to Israel.