iDevices almost never ship with a decent enough DAC and headphone amp on par with the iPod Classics. They are also subject to noise from circuitry which can be audiable if you have very sensitive gears.
The era with the 30-pin connector had an alternative route since one (or two?) of the pins were responsible for analog audio line out, originally intended for iPod docks and speakers. There were quite many HiFi equipments at that time taking advantage of this. But since Lightning is entirely digital, so you must use an external DAC via Lightning, or Lightning headphones etc which has built-in DAC+amp.
There are very few DACs out there with exclusive Lightning connectivity, so the most common way is to use a Lightning to USB dongle, or the USB3 Camera kit (which has a USB3 port + another Lightning port) as a stop gap, and then you can freely use any DAC with USB1/2 connection (literally every DAC made within the decade).
I personally use a small dongle sized one, the Audioquest Dragonfly Red, which is enough to decode lossless signals up to 24-bit 96kHz , and 2.1V output to drive earphones or smaller sized headphones (<78ohm).
For more ambitious setup I got a Fiio E17, on specs it suggests a max. of 150ohm but I can drive my Bayerdynamic DT1990 (250ohm) with good results. Anything with higher impedance (like 600ohm) will require larger amplification that is probably too bulky to be portable. Also there are folks who would like to push for very high resolution PCM or even DSD which of course require even more ambitious gears.
Studio monitors can use a less portable DAC, if you use an integrated amp chances are it already has built-in USB DAC, it may even have Airplay (although the audio quality via Airplay it is questioned by some). Some bookshelf active speakers also have built-in DAC and USB input which you can plug directly into the Lightning-USB dongle.
There is also a very alternative approach that is wireless, you can use something like the A&K XB10, which is a portable Bluetooth receiver and it can even drive ear/headphones with its 2.5mm balanced output. Many people use this with the iPhone 7.
