But, reports CBS News Correspondent John Blackstone, the stone-cold case may have been solved.
A man just arrested for kidnapping the children so long ago is their own grandfather, Marvin Maple. He'd moved from Tennessee to San Jose, Calif., where he and the children lived under new names.
"We have never stopped loving them," their mother, Debbie Baskin, told reporters. "We have never stopped praying for them, and that was an answered prayer, just to know they were alive."
"We believe they were home-schooled to keep them from, one, registering in schools, giving social security, date of births, who their mother and father are, any type of information," says Rutherford County Sheriff's Department Cold Case Unit Lt. Bill Sharp.
Maple and his wife, who died two years ago, disappeared with Christi and Bobby after a nasty custody battle. They claimed the children had been sexually abused by their parents.
"These charges were false," says Dan Goodwin, a spokesperson for the sherrif's office. "No abuse had occurred."
"My feelings for my dad is that I hope he finds help. There is no punishment that could give us back 20 years," Debbie Baskin reflected.
Debbie and Mark are hoping for a reunion, but they understand their son and daughter may need time to adjust.
"They were only, they were seven and eight when they were kidnapped," Mark says, "so they have a memory of us. And I'm asking them to access that, jst to go back in their minds, and think about the times we had together as a family. They have been living a lie for 20 years."
Ernie Allen, president of the National Center for Missing and Exploited Children, says Mark has the right idea.
"You do it slowly, and you do it cautiously," Allen told co-anchor Maggie Rodriguez on The Early Show Friday. "We have a top psychologist who's involved in helping with the reunification. These kids will be talked to, and it's just a slow, cautious process.
"In situations like this, we don't know what they've been told over the past 20 years. We don't know what they believe, whether there's been a kind of brainwashing happening. So, you just have to be patient."
Allen says the case proves, "You just don't ever close these cases.You continue the search. And in this one, somebody in the public provided a key piece of information that led to the identification of these kids and their abductors."
The Baskin children are now 27 and 28, and still living in San Jose.
Authorities say they're doing well, both have successful careers, but are still trying to process all that's happened.
Marvin Baskin was expected to fly back to Tennessee Friday to face kidnapping charges.