I spent a couple of days this week hanging out with Michael Kors. Actually, the superstar designer, whose namesake fashion company has been on a tear since its 2011 initial public offering, probably didn’t know I was in the same room at the preeminent conference for CEOs in fashion apparel and retail we were both attending. But I did learn a lot from what he and many others shared in formal presentations and impromptu conversation.

What I learned is relevant to a wide swath of leaders across industries and across national borders.

Lesson 1: There is a race to understand the millennial generation — and so far no one is winning

Most people have focused on the proclivities of millennials — the generation born between around 1981 and 2002 — while on the job. But the bigger question revolves around what attracts them to a product or service. After all, the generation reared on smartphones and laptops will dwarf the previously dominant baby boomers in size and influence, and it will be the biggest generation of consumers for years to come.

The answer to that question, so far, is a mystery. At dinner one night a senior executive of a major retailer was thrilled to hear that my 22-year-old daughter loved the jeans she bought from that retailer. This executive was not just thrilled, but almost beside herself, because of the challenges this particular company had in breaking through to millennials.

Apparel designers and retailers know they’ve got to better understand the millennial customer, and they’re making a big effort to do so. The best know that the answers of the past are not necessarily the right ones today and into the future. You can’t sit on the sidelines and hope to magically figure this out either; you’ve got to be in the game.

Lesson 2: Adapting to the digital sales revolution is still a challenge

Everyone was talking about e-commerce and every retailer has a presence online. But then there’s a company like ASOS, the British online juggernaut that has amassed a $5 billion market capitalisation by selling dozens of brands to millions of customers in virtually every country in the world.

The problem is not that apparel retailers don’t understand the trend. They do. It’s just that they — like all incumbents in an industry — must disrupt many long-cherished assumptions to fully embrace the online opportunity. All of the sales growth in this industry is coming from online, so there’s really no option.

ASOS CEO Nick Robertson pulled no punches in his presentation. It was a wake-up call for the audience. But it’s the same one that should be ringing in the executive suites of companies in almost every industry.

The rise and incredible power of online business is not exactly news, yet even in 2013 there are plenty of companies that find the transition daunting.

Lesson 3: It’s not bricks and mortar versus online, it’s both

Despite all the costs associated with physical stores, people still like to shop in-person, still like to touch the product and still like to experience the process of buying.

Amazon — the giant of online sales (if not profits just yet) — has invested billions of dollars in bricks and mortar, via enormous cloud computing facilities and massive order-fulfilment warehouses. Google and eBay are also active in using their technological platforms to enable local stores to serve as mini-distribution centres.

Apple also has had a huge influence on retailers. Apple is teaching fashion retailers about the importance of mobile in the store (who needs cash registers when you can check out on an iPhone?), customer service (maybe not crew members wearing blue or red T-shirts, but plenty of knowledgeable help at the ready for customers) and strategy (setting up an online channel as a complement, not a replacement, for the store experience).

Lesson 4: Next-generation leaders come with some built-in advantages

Selling to their millennial peers. Building businesses on digital platforms. Is it possible that younger leaders are better positioned to capitalise on these trends?

Consider the online clothing retailer Nasty Gal. It is nothing short of a phenomenon. Founded by Sophia Amoruso seven years ago as a way to make some money selling vintage clothes on eBay, the company has grown to $100 million in revenue and is gaining even more momentum.

The company’s core customer is the millennial woman. Likely in her twenties, this shopper values brand uniqueness, online experiences and a deep immersion into all aspects of the brand. Founder Amoruso labelled this core customer as obsessed with the brand — and who wouldn’t like to have customers like that?

I was particularly struck with how Amoruso described the relationship of the company with the customer. The customer has a seemingly insatiable appetite for information about the clothes, so Nasty Gal continually updates the website with new content, including blogs. Social media, such as Pinterest and Instagram, in this context is not an add-on, or incidental to the marketing effort, but the core of it.

The contrast with how CEOs of more established brands discussed social media and communication millennial-style was striking. For the (usually older, male) CEOs, there were “pros and cons” to social media. For the 29-year-old Amoruso, that equation does not even enter the discussion. Social media is in her DNA and in the DNA of her customers. She doesn’t need to learn how to make social media work. Just as importantly, she doesn’t need to unlearn old habits that now get in the way. It’s who she is and it’s a huge advantage.

Each of these lessons is not specific to the fashion apparel and retail sectors. Hanging out with leaders in these companies has reinforced, for me, the wide applicability of what they are experiencing today.  Fashionistas are usually a season or two ahead of everyone else. But when it comes to leading the charge on millennials and digital, with rare exceptions like ASOS and Amoruso, they’re still figuring it out like everyone else.