If all you're doing is static DC, or combinatorial (static digital logic), maybe you won't ever need them...
Let's reflect on the definition!
Resistor: V = I*R
Volts and amps, static, DC (or instantaneous, anyway -- doesn't care if AC or DC, it's all the same, just a V and an I).
Capacitor: I = C * dV/dt
Or if you swap it around, dV/dt = I * 1/C so it looks like a resistance too. Volts and amps, but not actually volts, but the rate of change over time. What?
If you don't know any calculus, dV/dt doesn't mean much to you, or worse, it looks like this horrible nonsense from high tier math...
Just understand it's a velocity, how voltage changes over time. DC by definition has dV/dt = 0, it's static, it's unmoving. And thus, by definition, AC is moving, dV/dt != 0. (Well, it's okay for dV/dt to be zero from time to time -- a sine wave starts and stops periodically -- but it's not zero for all time, see.)
And finally,
Inductor: V = L * dI/dt
The change in current over time.
Anywhere you need to store and release energy, you use one of these. Anywhere you need a time constant, anything to do with AC, with frequency or time dependent stuff.
In a digital circuit, you might also need delay, because even a combinatorial circuit has race conditions. Propagation delays of gates, and different delays between gates, often result in 'runt' pulses, where some part of the circuit finishes "deciding" its state before others. During those pulses, the output is invalid (i.e., not equal to the static value of function(input)), and that invalid output state might go on to trigger other logic, inappropriately, and so on.
Indeed, the more fundamental concept is delay; an ideal (abstract) capacitor or inductor or resistor has no length or delay (or assumes infinite speed of light), which is silly. The delay of a signal down a wire manifests as equivalent inductance and capacitance (equivalent at low frequencies), and you can directly use this fact to create inductors and capacitors of modest value, or conversely, to use the L/C properties of a circuit to determine its size, or how small it needs to be for a particular purpose, etc.
Tim