There are various places on the body where it can be detected. Actually, heart rate can be taken at any spot on the body at which an artery is close to the surface and a pulse can be felt. Typical spots are the wrist, the neck and the chest. On the last, the heart rate is measured on the skin based on the basis of electrocardiographic (ECG/EEG) signals generated by a heart beat. The ECG signal is an electromagnetic signal originating from the heart’s muscles. It is detected on the chest by means of electrodes, which are in contact with the body at least at two points. The electrode placed closer to the heart serves as the actual measuring electrode, while the other electrode acts as a ground potential, relative to which the voltage generated is measured by the measuring electrode in time. In certain chest devices the electrodes are arranged in a belt.  See also Chapter 13: The Electrocardiogram, in Guyton, Arthur, C., Human Physiology and Mechanisms of Disease, third edition, W. B. Saunders Company, 1982, ISBN 4-7557-0072-8. For other details visit: http://www.topendsports.com/fitness/equip-monitors.htm

How are pulses counted? Using a simple threshold crossing or something more sophisticated?

You must filter the signal. You can use FIR / IIR adaptive filtering, Kalman filtering, or spectral analysis methods. As a frequency estimate, I suppose that spectral analysis is more adequate. Computing power is no longer a problem for the new generations of low-power microcontrollers.

There are other approaches as well. Think of your (or a) smartphone. It measures the heart rate/beat with a camera and a flash, and the information is processed by an app. The process is photoplethysmography. When the heart sends a bloodpulse through the tiny capillary vessels, the skin surrounding them will expand.The smartphone's flash illuminates the skin and the pointed camera records the color changes that happen and that are hardly visible for a naked eye. This is however not a continuous heart beat monitoring. The processing is a kind of event orientated and it is needed to take a pulse about every 10 seconds.

Regardless of the measurement mode, won't heart rate estimation always be event oriented?

what event?

Generally speaking the measurement principles mentioned in previous posts do not estimate heart rate.

For example when using ECG to measure heart rate the peak electrical activity across cardiac tissue is measured against time. In the case of pulse oximeter (PPG) the peak volume of blood in a certain part of the body (usually finger) is measured against time. In short, heart rate is usually measured and rarely, to the best of my knowledge, estimated. 

In terms of event orientated, the heart reacts to certain neurotransmitters and biochemical markers that are released into the body and brain en masse when we register a change in our environment. This is how the body regulates the supply of blood to the different organs (i.e. Brain) in our body. 

For example when we are presented with a life threatening event our body is flooded with adrenalin while our brain is flooded with nano-adrenalin. In turn these neurotransmitters and biochemical markers cause the heart to beat quicker, transporting more blood, oxygen and nutrients around the body to the organs (i.e. muscles) that need it. 

A similar process occurs when were resting, sleeping, digesting etc. Although the neurotransmitters and biochemical markers will vary depending on the desired action, the heart (amongst other organs) reacts to the event the body encounters. 

So in short when our environment changes so to do the neurotransmitters and biochemical markers that regulate how the heart and our organs react. Some of these events have titles such as the flight or flight, rest and digest. They are phases that the body passes through during which the heart and other organs perform a certian task and can be viewed as event driven. 

Exceptions to this result in the body not functioning in a correct manner. One such exception, Orthostatic Hypotension occurs in people who've suffered damage to the autonomic nervous system or are consuming certian medications (i.e. L-DOPA). When people move from the supine position to upright, blood pools in lower limbs, blood pressure drops, heart rate fails to increase forcing vasovagal syncope (Fainting). In this case, the heart fails to responding correctly to the change in environment causing a change in homeostasis. Measuring heart rate during this phase would show a failure of the heart rate to adapt to an event the body encountered. 

The comments expose that the expectable accuracy/precision of measuring (or properness of estamation) is dependent not only on the place of measuring, but also on the method of detecting. In turn, the chosen method entails specific forms of information processing..