Will you trust a robot to manage your money—when you’re 64?

Companies that deliver automated online investment advisory services, the so-called robo-advisors, have proved they can effectively compete for investing dollars, taking in billions in investor assets in the past few years. That might not seem like much from the $16 trillion pie of individual investments, but it's already forced a response from investing heavyweights, including Charles Schwab, Vanguard and Fidelity.

Their success, they like to sometimes quip, comes from clients who prefer to never deal with a human or receive a phone call. That works in the early days of the era of the digital native, but will it still work when the digital natives turn 64?

As younger investors create families with greater financial complexity, including mortgages and the prospects of multiple college tuition bills, will they still trust a robot to manage their money?

The robo-advisors, not surprisingly, exude confidence.

"I feel absolutely confident that we can handle more complicated financial lives," said Jon Stein, CEO of Betterment.

Stein is not alone. Robo-advisors are working to address more complicated financial situations, whether that involves things like an inheritance, college savings or estate planning. They either are improving their automated services or providing on-staff experts who can give the kind of personalized attention that typically has been the domain of certified financial planners.

Read MoreRobo-advisors have yet to prove their worth: Analysts

Robo-advisors collectively manage an estimated $20 billion, which is predicted to reach $450 billion worldwide by 2020, according to research firm MyPrivateBanking in its recent 2015 report on the ways in which robo-advisors are infiltrating the wealth management industry.

Along with providing automated, algorithm-based portfolio management advice, some offer automatic portfolio rebalancing, tax-loss harvesting and other online tools that help clients determine how to invest their money.

One of their biggest appeals is what they charge clients: less than the industry standard of 1 percent of assets managed.

"It's a digital delivery that's cheaper and faster," said Will Trout, a senior analyst for research and consulting firm Celent. "But in terms of the more complex things, [robos] are taking baby steps."

Adam Nash, president and CEO of Wealthfront, is unconcerned, espousing the faith in tehcnology that you would expect from a Silicon Valley executive. His company focuses squarely on millennials, and because the industry is in its infancy, Nash thinks the technological advances that will end up helping his clients 20 years from now are yet to be realized.

"We're open to providing anything that customers find important," Nash said. "But we'll probably do that through improved technology. We're incredibly bullish about what will be possible for us to do to meet the needs of [millennials]."

He added that Wealthfront has a team of certified financial analysts who can respond to client questions. But if a request is beyond what the team is equipped to do, they refer clients to, say, an accountant or an attorney.

At FutureAdvisor, Will Tuhacek is a senior wealth advisor. He spends much of his days talking to clients, whose investments—regardless of where they are held—are tracked at the company.

"We can do a high-level review of their portfolio and all of their accounts. That allows us to make recommendations [about their financial profile]," Tuhacek said. "So is that [certified financial planner] advice? Partly. Full advice? No."

But, he added, having staff on hand to answer financial-planning questions is the direction in which the company wants to go.

At Betterment, if a client's situation is complicated, the company will refer the person to an in-house CFP—if the assets held there are at least $1 million. Alternatively, a client can be referred to an outside advisor who uses Betterment's institutional platform. Roughly 100 investment advisory firms use Betterment's platform for their clients, including fund and brokerage giant Fidelity Investments.

Financial services behemoths also have entered the space to varying degrees. Vanguard Group, which eschews the robo-advisor term, views its new Personal Advisor Services platform as a hybrid approach. It offers technological tools online but also gives clients access to human advisors.

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"It incorporates a relationship with an advisor on an ongoing basis," said Katie Henderson, a Vanguard spokeswoman.

Vanguard's service requires a minimum of $50,000. The company has about 300 full-time advisors on staff. The majority of them are CFPs; those who are not CFPs are working toward earning that designation, Henderson said.

Charles Schwab launched its robo platform, called Schwab Intelligent Portfolios, in March. The service requires a $5,000 minimum investment, which gives the client access to personal advice.

"When life gets more complicated, people often prefer a conversation to an interface," said Naureen Hassan, a Schwab executive vice president and head of Schwab Intelligent Portfolios, in response to an email query.

She added that clients have access to people and to financial planning. "It's a critical component of what Schwab can provide and people need," she said.

Regardless of the big names being in the space, the smaller robos feel well positioned to meet the needs of investors, no matter what their age or financial profile. And their services might not include traditional human advice.

Nash, of Wealthfront, pointed out that Schwab evolved from a discount brokerage 40 years ago to a major player in the money-management business. And, he said, no one could have predicted that. His message is, basically, don't discount the impact that technology will have on the investment and financial-planning world.

"Over the next five, 10 or 25 years," Nash said, "We'll see a phenomenal improvement in technology that will help people reach their financial goals."

—By Sarah O'Brien, special to CNBC.com